U.S. patent number 7,076,409 [Application Number 11/005,834] was granted by the patent office on 2006-07-11 for system and method for abstracting and visualizing a route map.
This patent grant is currently assigned to Microsoft Corporation. Invention is credited to Maneesh Agrawala, Chris Stolte.
United States Patent |
7,076,409 |
Agrawala , et al. |
July 11, 2006 |
**Please see images for:
( Certificate of Correction ) ** |
System and method for abstracting and visualizing a route map
Abstract
A system and method for placing an annotation or label in a
route map in an appropriate grid cell are described. Initially, the
route map is partitioned into an initial grid; composed of
candidate grid cells, into which the annotation or label can be
placed. If necessary, a search for grid cells having sufficient
adjacent object free grid cells is conducted. When no candidate
grid cells are found during the identifying or searching stages, a
grid subdivision scheme subdivides a portion of the grid cells in
the initial grid to form a new grid. Then, the identifying and
searching steps are repeated using the new grid. The process also
ranks multiple candidate cells based on a density of objects in
bordering grid cells. The candidate grid cell having the lowest
density of objects in bordering cells is selected as the
appropriate candidate grid cell.
Inventors: |
Agrawala; Maneesh (San
Francisco, CA), Stolte; Chris (Stanford, CA) |
Assignee: |
Microsoft Corporation (Redmond,
WA)
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Family
ID: |
27062795 |
Appl.
No.: |
11/005,834 |
Filed: |
December 6, 2004 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20050137791 A1 |
Jun 23, 2005 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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09727646 |
Nov 30, 2000 |
6952661 |
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09528703 |
Mar 17, 2000 |
6424933 |
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Current U.S.
Class: |
703/2; 701/454;
703/6; 715/232; 715/247 |
Current CPC
Class: |
G01C
21/367 (20130101); G01C 21/3673 (20130101); G06T
11/206 (20130101); G06T 11/60 (20130101); G06T
17/05 (20130101) |
Current International
Class: |
G06F
7/60 (20060101); G06F 17/10 (20060101) |
Field of
Search: |
;703/1-2,6-8
;701/201-212 ;715/517-521 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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PCT/US01/08439 |
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Mar 2001 |
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WO |
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Caricature," The Canadian Cartographer, vol. 10, No. 2, pp.
112-122. cited by other .
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Approximation of Plane Curves," Computer Graphics and Image
Processing, vol. 1,pp 244-356. cited by other .
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Graphics, Image Processing, and GIS, pp. 1-9. cited by other .
Visvalingam et al., "Line Generalisation by Repeated Elimination of
Points," Cartographic Information Systems Research Group,
University of Hull, pp. 46-51. cited by other .
Barkowsky et al., 2000, "Schematizing Maps: Simplification of
Geographic Shape by Discrete Curve Evolution," Spcial Cognition II,
LNAI 1849, pp. 41-53. cited by other .
Carpendale et al., 1995, "Three-Dimensional Pliable Surfaces: For
the Effective Presentation of Visual Information," Proceedings of
the ACM Symposium on User Interface Software and Technology, UIST
95:217-226. cited by other .
Cormen et al.,, "Introduction to Algorithms," Chapter 17, pp.
329-355. cited by other .
Edmondsen et al., 1997, "A General Cartographic Labeling
Algorithm," Cartographics 33:12-23. cited by other .
Markosian et al., "Real-Time Nonphotorealistic Rendering," In:
SIGGRAPH 97 Conference Proceedings (Aug. 1997), pp. 415-420. cited
by other .
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Illustrations," Computer Graphics 25(4): 123-132. cited by
other.
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Primary Examiner: Broda; Samuel
Attorney, Agent or Firm: Merchant & Gould P.C.
Parent Case Text
This application is a divisional of U.S. patent application Ser.
No. 09/727,646 filed Nov. 30, 2000 now U.S. Pat. No. 6,952,661,
entitled System And Method For Abstracting And Visualizing A Route
Map, which is a continuation-in-part of application Ser. No.
09/528,703 filed Mar. 17, 2000, now U.S. Pat. No. 6,424,933, the
disclosures of which are hereby incorporated herein by reference in
their entirety.
Claims
We claim:
1. A computer implemented method of placing an annotation or label
in a route map, said method comprising: partitioning said route map
into an initial grid that is composed of grid cells; identifying
candidate grid cells into which said annotation or label can be
placed, wherein each said candidate grid cell is a grid cell that
is free of objects associated with said route map; searching, when
said annotation or label will not fit in a single candidate grid
cell, for grid cells having sufficient adjacent object free grid
cells such that said candidate grid cell and one or more of said
adjacent object free grid cells can accommodate said annotation or
label; when no candidate grid cells are found in said identifying
or searching steps, performing a grid subdivision scheme, which
subdivides a portion of said grid cells in said initial grid to
form a new grid, and repeating said identifying and searching steps
using said new grid; ranking, when multiple candidate grid cells
are found, each candidate grid cell based on a density of objects
in grid cells that border each said candidate grid cell, wherein
the candidate grid cell that borders grid cells having the lowest
density of objects is selected as the candidate grid cell and all
other candidate grid cells are discarded; and positioning said
annotation or label in said candidate grid cell, thereby placing
said annotation or label in said route map.
2. The method of claim 1 wherein said grid subdivision scheme,
which subdivides a portion of said grid cells in said initial grid,
is a uniform spacial separation scheme.
3. The method of claim 1 wherein said grid subdivision scheme,
which subdivides a portion of said grid cells in said initial grid,
is a nonuniform spacial subdivision scheme.
4. The method of claim 1 wherein said annotation or label is
constrained to a subregion of said route map and said identifying
and searching steps are limited to said subregion.
5. The method of claim 4 wherein said portion of said grid cells in
said initial grid includes said subregion, and said grid
subdivision scheme comprises uniformly dividing each initial grid
cell into four uniformly sized grid cells.
6. The method of claim 4 wherein said subregion of said route map
is enlarged when no candidate grid cells are found in an instance
of said identifying and searching steps.
7. A computer program product executable on a computer system, the
computer program product comprising a computer readable storage
medium and a computer program mechanism embedded therein, the
computer program mechanism comprising: a map annotation module for
placing an annotation or label in a route map, said map annotation
module including: instructions for partitioning said route map into
an initial grid, said initial grid composed of grid cells;
instructions for identifying candidate grid cells into which said
annotation or label can be placed, wherein each said candidate grid
cell is a grid cell that is free of objects associated with said
route map; instructions for searching, when said annotation or
label will not fit in a single candidate grid cell, for grid cells
having sufficient adjacent object free grid cells such that said
candidate grid cell and one or more of said adjacent object free
grid cells can accommodate said annotation or label; instructions
for performing a grid subdivision scheme, when no candidate grid
cells are found after execution of said instructions for
identifying or said instructions for searching, said grid
subdivision scheme subdividing a portion of said grid cells in said
initial grid to form a new grid, and instructions for re-executing
said instructions for identifying and said instructions for
searching using said new grid; instructions for ranking, when
multiple candidate grid cells are found by said instructions for
identifying or said instructions for searching, said ranking of
each candidate grid cell dependent on a density of objects in grid
cells that border each said candidate grid cell, wherein the
candidate grid cell that borders grid cells having the lowest
density of objects is chosen as the candidate grid cell and all
other candidate grid cells are discarded; and instructions for
positioning said annotation or label in said candidate grid cell,
thereby placing said annotation or label in said route map.
8. The computer program product of claim 7 wherein said grid
subdivision scheme, which subdivides a portion of said grid cells
in said initial grid, is a uniform spacial separation scheme.
9. The computer program product of claim 7 wherein said grid
subdivision scheme, which subdivides a portion of said grid cells
in said initial grid, is a nonuniform spacial subdivision
scheme.
10. The computer program product of claim 7 wherein said annotation
or label is constrained to a subregion of said route map and said
instructions for identifying and said instructions for searching
are limited to said subregion.
11. The computer program product of claim 10 wherein said portion
of said grid cells in said initial grid includes said subregion,
and said grid subdivision scheme comprises uniformly dividing each
initial grid cell into four uniformly sized grid cells.
12. The computer program product of claim 10 wherein said subregion
of said route map is enlarged when no candidate grid cells are
found after execution of said instructions for identifying and
instructions for searching.
13. A computer system for optimizing a display of a route map, the
computer system comprising: a central processing unit; a memory,
coupled to said central processing unit; a viewport for displaying
said route map; a program module, executable by said central
processing unit, said program module comprising: instructions for
partitioning said route map into an initial grid, said initial grid
composed of grid cells; instructions for identifying candidate grid
cells into which said annotation or label can be placed, wherein
each said candidate grid cell is a grid cell that is free of
objects associated with said route map; instructions for searching,
when said annotation or label will not fit in a single candidate
grid cell, for grid cells having sufficient adjacent object free
grid cells such that said candidate grid cell and one or more of
said adjacent object free grid cells can accommodate said
annotation or label; instructions for performing a grid subdivision
scheme, when no candidate grid cells are found after execution of
said instructions for identifying or said instructions for
searching, said grid subdivision scheme subdividing a portion of
said grid cells in said initial grid to form a new grid, and
instructions for re-executing said instructions for identifying and
said instructions for searching using said new grid; instructions
for ranking, when multiple candidate grid cells are found by said
instructions for identifying or said instructions for searching,
said ranking of each candidate grid cell dependent on a density of
objects in grid cells that border each said candidate grid cell,
wherein the candidate grid cell that borders grid cells having the
lowest density of objects is chosen as the candidate grid cell and
all other candidate grid cells are discarded; and instructions for
positioning said annotation or label in said candidate grid cell,
thereby placing said annotation or label in said route map.
14. The computer system of claim 13 wherein said grid subdivision
scheme, which subdivides a portion of said grid cells in said
initial grid, is a uniform spacial separation scheme.
15. The computer system of claim 13 wherein said grid subdivision
scheme, which subdivides a portion of said grid cells in said
initial grid, is a nonuniform spacial subdivision scheme.
16. The computer system of claim 13 wherein said annotation or
label is constrained to a subregion of said route map and said
instructions for identifying and said instructions for searching
are limited to said subregion.
17. The computer system of claim 16 wherein said portion of said
grid cells in said initial grid includes said subregion, and said
grid subdivision scheme comprises uniformly dividing each initial
grid cell into four uniformly sized grid cells.
18. The computer system of claim 16 wherein said subregion of said
route map is enlarged when no candidate grid cells are found after
execution of said instructions for identifying and instructions for
searching.
Description
The present invention relates generally to a system and method for
generating a route map. More particularly, this invention relates
to a system and method for applying a unique scale factor to each
road in a route map and for optimizing the positions of labels in
the route map. Further, a method for rendering the appearance of
roads in the route map is disclosed.
BACKGROUND
Route maps, when well designed, are an effective device for
visualizing and communicating directions. Such maps have existed in
various forms for centuries, and the recent availability of
detailed geographic databases via the Internet has led to the
widespread use of computer-generated route maps. Online mapping
services typically provide directions as a set of maps complemented
with text descriptions. Such on-line computer-generated maps are
unsatisfactory, however, because the algorithms used to generate
the maps disregard many of the techniques and principles used by
human map-makers.
Effective use of a route map generally requires two distinct
activities: (i) following a path until reaching a critical point
and (ii) changing orientation at that point to follow another path.
Thus, one of the most important types of information route maps can
communicate are points of reorientation, that is, point along the
route where someone must consciously turn from one path to another.
However, existing computer-generated route maps fail to effectively
communicate points of reorientation because they scale all the
roads in the map by a constant scale factor. The scaling of all the
roads in a route map by a constant scale factor is referred to
herein as uniform scaling. As a result of uniform scaling, for
routes of any reasonable length, uniform scaling frequently
requires some roads to be very short. But it is often precisely
these very short roads that connect critical turning points. Thus,
uniform scaling can result in a loss of some of the most critical
information found in a route map.
Another shortcoming in prior art computer-generated route maps is
that they needlessly depict accurate length, angle, and curvature
of each road in the route. Such accurate depictions are made at the
expense of map readability. Psychological research indicates that
most people distort distances, angles, and curvature when drawing
route maps. See e.g., Tversky and Lee, "How space structures
language," Spacial Cognition: An interdisciplinary approach to
representation and processing of spacial knowledge, (eds.) Freska,
Habel, and Wender, 1998, 157 175; Tversky and Lee, "Pictorial and
Verbal Tools for Conveying Routes," COSIT 99, Conference
Proceedings, Stade Germany, 1999, 51 64. Other psychological
studies indicate that people maintain such distortions in their own
mental representations of a route. See e.g., Tversky, "Distortions
in Cognitive Maps," Geoforum 23, 1992, 131 138. Thus, adherence to
accurate lengths and angles in prior art computer-generated maps
runs counter to how humans conceptualize routes.
Computer-generated route maps can be classified into four major
mapping styles: route highlight maps, TripTiks, overview/detail
maps, and two dimensional nonlinear distortion maps. Route
highlight maps simply highlight the route on a general road map of
the region, as shown in FIG. 1. Since the purpose of general road
maps is to provide an understanding of the entire road system in a
region, such maps typically employ constant scale factors and
display extraneous detail throughout the map. The constant scaling,
as exhibited in FIG. 1, generally causes one of two problems.
Either detailed turn information is lost because the scale factor
is too large, or the scale factor is small enough to show the
detail, but the map is very large. Since general road maps are not
optimized to show any particular route, a route highlight map will
often suffer from both a large scale factor and an inconvenient
size. The clarity of the route in a route highlight map depends on
the style of the highlighting since that is the only property
differentiating the route from other roads. Usually the route is
distinctively colored, but because general road maps provide
context information over the entire map, the map is cluttered with
extraneous information that makes it difficult to perceive the
route and the individual reorientation points.
TripTiks are similar to route highlight maps, but they are
specifically designed for communicating a particular route. As
shown in FIG. 2, a TripTik map usually stretches over multiple
rectangular pages, and each page is oriented so that the route runs
roughly down the center of the page. Each TripTik page employs
constant scaling, but the scale factor differs across pages.
Changing the scale factor from page to page allows the TripTik to
show more detailed turn information where needed. However, because
the map stretches over many pages and the orientation and scale
factor varies from page to page, forming a general understanding of
the overall route is difficult.
Overview/detail maps combine multiple maps rendered at different
scales to present a single route, as shown in FIG. 3. One of the
maps (e.g., FIG. 3A) is scaled by a large factor so that it
provides an overview of the entire route. Since the large scale
factor of this map reduces the readability of local turn details,
maps showing-turn-by-turn information are provided (e.g., FIG. 3B).
A constant scale factor is used for each map, but the scale factor
differs across the maps. While an overview/detail map may seem like
an effective combination, such maps are unsatisfactory in practice.
The overview map rarely presents more than the overall direction
and context of the route. Although turn-by-turn maps provide
detailed information for every turn, the use of distinct maps for
each turn, often with different orientation and scale, makes it
difficult to understand how the maps correspond to one another.
Therefore, the navigator has difficulty forming a cognitive model
of the route.
To ensure clear communication of all of the reorientation points,
some parts of a route's depiction may require a small scale factor
while others require a large scale factor. Researchers have
described attempts to use two dimensional nonlinear image
distortion techniques on general road maps to provide
focus-plus-context viewing. (See. e.g., Carpendale et al.,
"Three-Dimensional Pliable Surfaces: For the Effective Presentation
of Visual Information," Proceedings of the ACM Symposium on User
Interface Software and Technology, UIST 95, 1995, 217 226; Keahey,
"The Generalized Detail-In-Context Problem," Proceedings of the
IEEE Symposium on Information Visualization, IEEE Visualization
1998). These techniques allow users to choose regions of the map
they want to focus on and then apply a nonlinear magnification,
such as a spherical distortion, to enlarge these focus regions.
Such two dimensional distortion allows detailed information to be
displayed only where relevant and often produces general area maps
that can be conveniently displayed on a single page. However, a
major problem with nonlinear two-dimensional distortion is that the
regions at the edges between the magnified and non-magnified
portions of the map undergo extreme distortion.
In an effective route map, all essential components of the route,
especially the roads, are easily identifiable. The route is clearly
marked and readily apparent even at a quick glance. The map
contains only as much information as is necessary and is easy to
carry and manipulate. To further such design goals, map content,
precision, and rendering style must be carefully optimized. Map
content includes important parameters such as a route start and
end, as well as points of reorientation. Although all maps are
abstract representations of a route, there is a range of styles
that can be used to render a map, with varying associations of
accuracy and realism. An appropriate rendering style can greatly
affect the readability and clarity of a map. Retinal properties
such as color and line thickness are used to draw attention to
important features of the map. Rendering style can also aid the
user in interpreting how closely the map corresponds with the real
world. Another important map design goal is the proper use of
context information. The amount of context information included in
the map greatly affects the utility of the map. Useful context
information includes labels or names for a path on the route as
well as context information along the route such as buildings, stop
lights, or stop signs. When drawing a route map by hand, people
most commonly use context information to indicate points of
reorientation and, less frequently, to communicate progress along a
road.
Environmental psychology studies have demonstrated that human
generated route maps contain distortion. There are three primary
types of distortion: (1) inaccurate path lengths, (2) incorrect
turning angles at intersections, and (3) simplified road shape. For
example, Tversky and Lee, COSIT 99 Conference Proceedings, 1999, 51
64, asked a group of students to sketch a route map between two
locations near the Stanford University campus. Although they
encouraged participants in their study to represent paths and
intersections accurately, most did not. Most intersections were
drawn at right angles regardless of their actual angle and
seventy-one percent of the participants used simple generic curves
and straight lines to represent roads. Even when participants
intended to communicate the shape or length of the road accurately,
they typically rendered these attributes incorrectly. Such
distortion in the map is in fact beneficial because it increases
the flexibility available to the map-maker in the design and layout
of the map. Variably scaling the length of each road allows the
map-maker to ensure all reorientation points are visible, while
flexibility in choosing turning angles and road curvature allows
the map to be simplified. Such distortions can simultaneously
improve the readability and convenience of the route map with
little adverse effect on its clarity and completeness.
Hand-drawn route maps often present a good combination of
readability, clarity, completeness and convenience, as shown in
FIG. 4. Instead of using a constant scale factor, hand-drawn maps
only maintain the relative ordering of roads by length. While this
ensures that longer roads appear longer than shorter roads in the
map, each road is scaled by a different factor. Often the map
designer does not know the exact length of the roads and only knows
their lengths relative to one another. The flexibility of relative
scaling allows hand-drawn route maps to fit within a manageable
size and remain readable.
Hand-drawn route maps typically remove most contextual information
that does not lie directly along the route. This strategy reduces
overall clutter and improves clarity. The intersection angles in
hand-drawn maps are generally incorrect, the precise shape of roads
is often misrepresented, and the roads are typically depicted as
generically straight or curved. These distortions make the map
simpler and only remove unnecessary information. Hand-drawn route
maps are rendered in a "sketchy" style typical of quick pen-and-ink
doodling. Many navigators are familiar with such hand-drawn maps
and the sketchy style is a subtle indicator of imprecision in the
map.
In order to improve route map clarity, many algorithms have been
developed for smoothing, interpolating, and simplifying roads in a
route map. In the area of map rendering the most well-known
simplification algorithms are Douglas & Peucker, "Algorithms
for the reduction of the number of points required to represent a
digitized line or its caricature," The Canadian Cartographer 10(2),
1973, 112 22; Ramer, "An iterative approach for polygonal
approximation of planar closed curves," Computer Graphics and Image
Processing. 1, 1972, 244 56; Visvalingam & Whyatt, "Line
generalization by repeated elimination of points," Cartographic
Journal. 30(1), 1993, 46 51; and Barkowsky, Latecki, and Richter,
"Schematizing maps: Simplification of geographic shape by discrete
curve evolution, " in Freksa, Brauer, Habel, and Wender (eds.):
Spacial Cognition II, Springer-Verlag, Berlin, in press. Given a
piecewise linear curve as a set of shape points, all of these
methods remove some subset of the shape points to produce a simpler
curve. Examples of shape points 3302 and turning points 3306 are
provided in FIG. 33A. Each of these methods uses different
criteria/metrics to decide which shape points to remove and which
to retain. As roads become simpler both the perceptual benefits and
processing speed increase. The most extreme form of simplification
replaces the piecewise linear road with a single linear segment
from the first shape point to the last shape point. Although this
extreme approach produces a good approximation in most cases, it
can cause the map to become misleading. Prior art algorithms for
simplifying roads in a route map can generate three types of
undesirable results:
(i) False Intersections. Roads that did not intersect before
simplification falsely intersect after simplification. An example
of a false intersection 3310 is found in FIG. 33A.
(ii) Missing Intersections. Roads that did intersect before
simplification no longer intersect after simplification. An example
of a missing intersection 3312 is found in FIG. 33B.
(iii) Inconsistent Turning Angles. The turning angle between roads
can change substantially, even to the point where a left turn might
appear as a right turn. An example of a wrong turn angle 3314 is
found in FIG. 33C.
Based on the above background it is apparent that what is needed in
the art is an improved system and method for making
computer-generated maps. What is further needed in the art is a
system and method for making computer generated maps that avoid the
pitfalls found in existing map-making algorithms, such as the use
of extraneous information and constant scaling.
SUMMARY OF THE INVENTION
The present invention provides an improved system and method for
making computer-generated maps. In the present invention, each road
in a route is individually scaled. The scale factor for each road
is optimized using an objective function that considers a number of
factors such as the number of false intersections and the number of
roads that are shorter than a minimum threshold length. Thus, the
scaled route fits in a predetermined viewport without loss of
information about important turns. Refinement against the objective
function is performed by one of many possible search algorithms
such as greedy searches, simulated annealing schedules, or gradient
descents. Greedy search algorithms are described in Cormen et al.,
Introduction to Algorithms, eds. Cormen, Leiserson, & Rivest,
The MIT Press, Cambridge Mass., 1990, 329 355. Simulated annealing
was first disclosed by Kirkpatrick et al. in the article
"Optimization by Simulated Annealing," Science 220 1983, 671 680.
Unlike prior art methods, some embodiments of the present invention
provide simplification algorithms that ensure that problems such as
false intersections, missing intersections, and inconsistent
turning angles do not occur in the final scaled route map.
Map clutter in the scaled map is avoided by refining label
positions against a novel target function that minimizes the number
of roads the labels intersect, the number of labels that intersect
each other, and the distance along the route between a label and
the center of a road corresponding to the label. In one embodiment,
simulated annealing is used to find a solution to the novel target
function. The final scaled route map is rendered so that it has the
appearance of a hand-drawn map. The rendered map clearly
communicates every reorientation point in a readable and convenient
form.
One embodiment of the present invention provides a method for
rotating the route map to best fit the display aspect ratio. In
this method, a collection of reference points in the route map are
defined. Each reference point in the collection corresponds to a
position of an intersection in the route map. The collection of
reference points form a distribution in two dimensional space.
Therefore, they can be fitted with a probability distribution
function that defines the mean position of the collection of
reference points in the two dimensional space as well as the
farthest position in which a member of the collection of reference
points extends in a first direction away from the mean position
(i.e. a first extent) as well as the farthest position to which a
member of the collection of reference points extends in a direction
that is orthogonal to the vector between the mean position and the
position of the first extent (i.e. a second extent). The mean,
first extent, and second extent provide a description of the outer
boundary of the reference points and a bounding box that denotes
this outer boundary is computed. The bounding box is centered on
the mean position and the sides of the bounding box are determined
by the positions of the first extent and the second extent. The
orientation of the bounding box is determined by the vector between
the mean position and the position of the first extent. Based on
this orientation, the route map is rotated by an amount that is
sufficient to reorient the bounding box to a predetermined
orientation, thus forming a rotated route map. A portion of the
rotated route map is then presented, thereby optimizing the display
of the route map.
Another embodiment of the present invention provides a method for
placing an annotation or label in a route map. In the method, the
route map is partitioned into an initial grid. The grid is composed
of grid cells. Candidate grid cells, into which the annotation or
label can be placed, are identified. Each of the candidate grid
cells are free of objects associated with the route map. When the
annotation or label will not fit in a single candidate grid cell, a
search for grid cells having sufficient adjacent object free grid
cells is conducted. This search is subject to the requirement that
the candidate grid cell, and one or more of the adjacent object
free grid cells, must be able to accommodate the annotation or
label. When no candidate grid cells are found during the
identifying or searching stages, a grid subdivision scheme is
performed. The grid subdivision scheme subdivides a portion of the
grid cells in the initial grid to form a new grid. Then, the
identifying and searching steps are repeated using the new grid.
When multiple candidate grid cells are found, each candidate grid
cell is ranked based on a density of objects in grid cells that
border each candidate grid cell. The candidate grid cell that
borders grid cells having the lowest density of objects is selected
as the candidate grid cell and all other candidate grid cells are
discarded. The annotation or label is positioned in the candidate
grid cell, thereby placing the annotation or label in the route
map.
In another embodiment of the present invention, a plurality of
labels are positioned in a route map. For each label in the
plurality of labels, the following steps are performed:
(i) A plurality of constraint-definitions are associated with the
label. Each constraint definition in the plurality of constraint
definitions uniquely defines a bounding box, label orientation, and
layout style.
(ii) An initial constraint definition is selected from the
plurality of constraint definitions.
(iii) A center of the label is positioned at a location within the
bounding box defined by the initial constraint definition in
accordance with the label orientation and layout style defined by
the initial constraint definition.
The method further comprises choosing a label in the plurality of
labels and determining a first score (S.sub.1) using a target
function. The target function is determined by a position of the
chosen label in the route map. Then, a constraint definition is
selected from the plurality of constraint definitions associated
with the selected label. The selected constraint definition is then
applied. Application of the constraint definition includes the step
of repositioning the center of the label inside the bounding box
defined by the constraint definition, in accordance with the label
orientation and layout style defined by the constraint definition.
A second score (S.sub.2) is calculated using a target function that
considers the repositioned label position. The new position for the
label is accepted in accordance with a function that is determined
by a comparison of S.sub.1 and S.sub.2. The choosing, determining,
applying, calculating, and accepting steps are repeated until a
first occurrence of an exit condition. Exemplary exit conditions
include achievement of a suitably low score or the occurrence of a
predetermined number of repetitions of the choosing, determining,
applying, calculating, and accepting steps.
Still another embodiment of the present invention provides a method
of preparing a route map that describes a path between a start and
an end. In this method, the path from the start to the end is
obtained. The path comprises an initial set of elements. Each
element includes sufficient information to determine a direction.
Further, each element intersects at least one other element in the
initial set of elements. A first element in the initial set of
elements includes a start and a second element in the set includes
the end. A different scale factor is independently applied to each
of at least two elements in the initial set of elements.
Application of the different scale factor to each of the at least
two elements produces a scaled set of elements. A total height and
a total width of a rendering of each element in the scaled set of
elements is estimated. Then, an image component is selected based
on a function of the total height and the total width. Finally, an
image of the scaled route map is formed by rendering each element
in the scaled set of elements.
Another embodiment of the present invention includes a method of
adding a cross street, and a cross street label associated with the
cross street, to a route map that includes a main path. In the
method, an intersection point at which the cross street intersects
the main path is determined. The cross street is placed in the
route map with the constraint that the cross street intersects the
main path at a first test position that is randomly chosen from a
segment of the main path that includes the intersection point. The
cross street label is positioned at a second test position within a
predetermined area. The predetermined area includes the
intersection point. A length of the cross street is adjusted so
that the cross street passes under the cross street label and
intersects the main path. The first or second test position is
perturbed by an random amount and a score of a function, i.e.
scoring function, is obtained. The size of the random amount used
to perturb the first or second test position is typically a small
increment that is designed to see if a "tweak" in the first or
second test position leads to an improved score. However, on
occasion, the size of the random amount used to perturb the first
or second test position is considerably larger, in order to prevent
the scoring function from becoming trapped in a local minima. The
scoring function is determined by a location of the cross street
and the cross street label in the route map. The perturbing and
obtaining steps are repeated until the score reaches a threshold
value or the perturbing and obtaining steps have been executed a
predetermined number of times. The cross street and the cross
street label are added to the route map when the score reaches the
threshold value. Furthermore, the cross street and the cross street
label are not added to the route map when the perturbing, obtaining
and determining steps have been executed the predetermined number
of times before the score has reached the threshold value.
In still another embodiment of the present invention, a method of
preparing a route map that describes a path between a start and an
end is provided. In this method, the path from the start to the end
is obtained. The path comprises an initial set of elements. Each
element includes sufficient information to determine a direction
and each element intersects at least one other element in the
initial set of elements. A first element in the initial set of
elements includes the start and a second element in the initial set
of elements includes the end. A different scale factor is
independently applied to each of at least two elements in the
initial set of elements. Application of the different scale factor
to each of the at least two elements produces a scaled set of
elements. A rendering of each element in the scaled set of elements
is created to form an intermediate map. A set of N breakpoints is
identified in the intermediate map. Each breakpoint in the set of N
breakpoints occurs in an element in the scaled set of elements, and
a minimum value for N is determined by the expression:
N>=S/M
where, S is a number of elements in the scaled set of elements; and
M is a predetermined maximum number of elements. The intermediate
map is then split into a set of N segment maps, each segment map
including a different breakpoint. The set of N segment maps thereby
comprises the route map.
Another embodiment of the present invention provides a method of
simplifying a road in a route map. In the method, the road is
approximated as a piecewise linear curve that includes a plurality
of shape points. Each shape point in the plurality of shape points
is connected by a linear segment to a respective shape point in the
plurality of shape points. At least one point at which the road
intersects another road in the route map is added to the plurality
of shape points as an intersection point. Each shape point in the
plurality of shape points that is (i) not a first shape point, (ii)
a last shape point, or (iii) an intersection point, is marked. A
check is made for false intersections between the road and another
road in the route map and, when a false intersection is found, a
first marked shape point and a last marked shape point in the
plurality of shape points are unmarked. The checking step is
repeated until no false intersection is found or there is no marked
shape point in the plurality of shape points. When a shape point is
marked, the piecewise linear curve is modified by replacing the
marked shape point and each said linear segment connected to the
marked shape point with a new linear segment that originates at a
shape point or intersection point immediately proceeding the marked
shape point and ends with a shape point or intersection point
immediately succeeding the marked shape point. When a shape point
is unmarked, the piecewise linear curve is modified by replacing
the new linear segment associated with the shape point with (i) a
first linear segment that is bounded by the shape point or
intersection point immediately proceeding the marked shape point
and the shape point and (ii) a second linear segment that is
bounded by the shape point or intersection point succeeding the
marked shape point and the shape point. In this way, the piecewise
linear curve represents a smoothed road that corresponds to the
road in said route map.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a prior art route highlight map.
FIG. 2 is a prior art TripTik map.
FIG. 3 is a prior art Overview/Detail map.
FIG. 4 is a prior art hand-drawn map.
FIG. 5 is a map that is generated in accordance with one embodiment
of the present invention.
FIG. 6 illustrates a system for generating a route map in
accordance with one embodiment of the present invention.
FIG. 7 illustrates the processing steps used to optimize the length
of individual roads in a route map using a greedy algorithm, in
accordance with one embodiment of the present invention.
FIG. 8 illustrates the processing steps used to optimize the length
of individual roads in a route map using a simulated annealing
schedule, in accordance with one embodiment of the present
invention.
FIG. 9 illustrates the processing steps used to optimize label
positions in a route map using a simulated annealing schedule, in
accordance with one embodiment of the present invention.
FIG. 10 illustrates a map before and after road extensions are made
so that labels are optimally associated with corresponding
roads.
FIGS. 11A, 11B, and 11C illustrate the conceptual steps used to
identify the longest axis of a route and to rotate this axis in a
predetermined direction, in accordance with one embodiment of the
present invention.
FIG. 12 illustrates a generalized problem of placing annotations on
a route map.
FIG. 13 illustrates the processing steps associated with one
solution to the generalized problem of placing annotations in a
route map in accordance with one embodiment of the present
invention.
FIG. 14 illustrates the spacial subdivision of a route map in order
to identify regions of the route map that are suitable for the
placement of annotations as well as labels.
FIG. 15 illustrates a generalized problem, which arises in a
spacial subdivision approach to placing a label or annotation in a
constrained area, in which no empty grid cell can be found.
FIG. 16 illustrates how nonuniform subdivision is used to solve the
problem of using spacial subdivision to place a label or annotation
in a constrained area.
FIGS. 17A and 17B illustrate the use of bounding boxes and FIGS.
18A and 18C illustrate the use of orientation vectors that are
present in some constraint definitions in accordance with one
embodiment of the present invention.
FIGS. 18A, 18B, 18C, 18D, 18E, and 18F illustrate various layout
styles that are present in some constraint definitions in
accordance with one embodiment of the present invention.
FIG. 19 illustrates the processing steps used to optimize label
positions in a route map using a simulated annealing schedule that
includes usage of constraint definitions, in accordance with one
embodiment of the present invention.
FIG. 20 provides an overview of an embodiment of layout module 688
that makes use of expanded constraint definitions, in accordance
with one embodiment of the present invention.
FIG. 21 illustrates exemplary image components and text boxes used
to compose forms, in accordance with one embodiment of the present
invention.
FIGS. 22A, 22B, and 22C illustrate various output forms in
accordance with one embodiment of the present invention
FIG. 23 illustrates a scaled route map with cross streets in
accordance with one embodiment of the present invention.
FIG. 24 illustrates the general problem of determining an amount of
visual clutter in a pixel based image of a route map.
FIG. 25 illustrates a route map with several point features, such
as exit numbers, restaurant locations, and city names included in
accordance with one embodiment of the present invention.
FIG. 26 illustrates a cluttered route map that would be difficult
to use while driving.
FIG. 27 illustrates the route map of FIG. 26 split into two segment
maps which, taken together, comprise the route map of FIG. 26.
FIGS. 28A, 28B, 28C and 28D illustrate various intermediate and
segment maps in accordance with one embodiment of the present
invention.
FIG. 29 illustrates a scaled route map with a corresponding inset
in accordance with one embodiment of the present invention.
FIG. 30 illustrates how the use of an inset can be used to avoid
the circularization of a predominantly North-South or East-West
route map in accordance with one embodiment of the present
invention.
FIG. 31 illustrates how the use of an inset can be used to
associate legible labels to roads that do not have legible labels
in a corresponding main route map, in accordance with one
embodiment of the present invention.
FIG. 32A illustrates a route map before curve (road or element)
simplification and FIG. 32B illustrates the route map of FIG. 32A
after curve simplification, in accordance with one embodiment of
the present invention.
FIG. 33 illustrates how road simplification can introduce false
intersections (33A), missing intersections (33B), and inconsistent
turning angles (33C).
FIG. 34 illustrates how a road is treated as a set of shape points
(s) into which intersection points are introduced, in accordance
with one embodiment of the present invention.
FIG. 35 illustrates the intersection of roads r.sub.1 and r.sub.2
at a point 3502.
FIGS. 36A and 36B respectively illustrate two different methods for
identifying shape points to remove or retain from roads in a road
map that are not part of a ramp, in accordance with one embodiment
of the present invention.
FIG. 37 illustrates aspects of shape points in a ramp that are
measured in order to evaluate a relevance of a particular shape
point in a ramp in a route map during a simplification process, in
accordance with one embodiment of the present invention.
FIG. 38 illustrates shape points in a ramp in a route map, in
accordance with one embodiment of the present invention.
FIG. 39 illustrates how a check for turn angle consistency is made
when considering to drop a ramp from a route map, in accordance
with one embodiment of the present invention.
FIGS. 40A and 40C illustrate portions of an unscaled route map
whereas FIGS. 40B and 40D show corresponding scaled route maps that
respectively illustrate how scaling can lead to false intersections
and missing intersections.
FIG. 41A illustrates how a missing intersection is scored and FIG.
41B illustrates how a misplaced intersection is scored in
accordance with one embodiment of the present invention.
FIGS. 42A, 42B, and 42C illustrate several false intersection
scenarios, showing for each false intersection point which
direction the closest endpoint must travel to remove the knot
formed by that false intersection point.
FIG. 43 illustrates a knot that is produced by a false intersection
upon scaling a route map.
FIGS. 44A and 44B illustrate methods for resolving false
intersections, in accordance with various embodiments of the
present invention.
FIGS. 45A and 45B illustrate two types of missing intersections
that arise during route map scaling.
FIGS. 46A and 46B illustrate methods for resolving missing
intersections, in accordance with various embodiments of the
present invention.
FIGS. 47A and 47B illustrate the utility of using extended
intersections, in accordance with one embodiment of the present
invention.
FIG. 48 illustrates how an extended intersection may work against
the resolution of a false intersection during route map
refinement.
FIG. 49 illustrates a way to determine which extended intersections
to add to a refinement score, in accordance with one embodiment of
the present invention.
Like reference numerals refer to corresponding parts throughout the
several views of the drawings.
DETAILED DESCRIPTION OF THE INVENTION
The present invention provides a system and method for generating
maps that have the benefits and characteristics of a hand-drawn
map. Automatically generating route maps in this style is complex.
Distorting aspects of the map can accentuate reorientation points,
but it can also have detrimental effects such as introducing false
intersections. Creating an effective route map generally requires
searching a large space of possible map layouts for an optimal
layout. An efficient multistage algorithm that couples a road
layout refinement module with a label and annotation placement
module is disclosed. The resulting map is rendered using subtle
perceptual cues, such as a wavy hand-drawn style for drawing the
paths, to communicate the distortion of scale and shape.
The design goals of the present invention are:
(i) Roads should be variably scaled so that all roads and
reorientation points are clearly visible and easily labeled.
(ii) If road A is longer than road B, then road A should be
noticeably longer than road B in the map.
(iii) The representation of a road only needs to convey general
curvature and the significant changes in orientation.
(iv) The precise angle of intersection of two roads is not
important; instead it is sufficient to communicate clearly the
action to be taken (turn left; turn right) and a generalized
orientation.
(v) The start and end of the route should be clearly marked.
(vi) A "sketchy" style should be used to render a road in order to
represent an imprecision of scale and orientation.
(vii) The resulting map should fit in the desired viewport, such as
a single sheet of paper, a computer display screen and/or a window
in a graphical user interface.
Generating a computer-based map in accordance with the above
identified design goals is more difficult than generating a map in
conventional computer-based styles. Variable road scaling provides
some flexibility in choosing the length of each road to produce a
clear and readable map. However, the relative ordering of roads by
length must remain fixed and false intersections should not be
introduced into the map. The space of all possible route-map
layouts is extremely large, and therefore it is not feasible to
blindly search for a layout that satisfies the design goals of the
present invention. Rather, a multi-phase heuristic
generate-and-test approach is used to obtain a map that satisfies
the design principles of the present invention. FIG. 5 illustrates
a map generated using the methods of the present invention.
General Architecture
Attention now turns to FIG. 6, which is a system in accordance with
one embodiment of the present invention. FIG. 6 illustrates a
network 620 that is operated in accordance with the present
invention. Network 620 includes at least one user computer 622 and
at least one server computer 624. User computer 622 and server
computer 624 are connected by transmission channel 626, which may
be any wired or wireless transmission channel.
User computer 622 is any device that includes a Central Processing
Unit (CPU) 630 connected to a random access memory 650, a network
connection 634, and one or more user input/output ("i/o") devices
638 including output means 640. In some embodiments, system memory
650 includes read-only memory (ROM). Output means 640 is any device
capable of communicating with a human and includes, for example, a
monitor, voice user interfaces, and/or integrated graphic means
such as mini-displays present in web-phones. Typically, user
computer 622 includes a main non-volatile storage unit 636,
preferably a hard disk drive, for storing software and data.
Further, user computer 622 includes one or more internal buses 632
for interconnecting the aforementioned elements. In a typical
embodiment, memory 650 includes an operating system 652 and an
Internet browser 654.
In some embodiments of the present invention, user computer 622 is
a hand held device such as a Palm Pilot. Accordingly, in such
embodiments, it is possible that user computer 622 does not have
disk 636 and browser 654 is integrated seamlessly into operating
system 652.
Server computer 624 includes standard server components, including
a network connection device 660, a CPU 662, a main non-volatile
storage unit 664, and a random access memory 668. Further, server
computer 624 includes one or more internal buses 666 for
interconnecting the aforementioned elements. Memory 668 stores a
set of computer programs, modules and data to implement the
processing associated with the invention. In particular, a
preferred embodiment of memory 668 includes an operating system 680
and a HTTP server 682. Memory 668 further includes direction parser
684, road layout module 686, label layout module 688, annotation
module 690, and map renderer module 692. In some embodiments of the
present invention, memory 668 also includes a direction database
694 and/or context database 696. As will be discussed in further
detail below, server computer 624 further includes a shape
simplification module 697 for smoothing roads in a route map, a map
verticalization module 698 for optimizing the dimensions of a
scaled route map to the dimensions of the viewport used to display
the scaled route map, and a map division module 699 for breaking a
complex scaled route map into a plurality of segment maps.
Direction parser 684 reads directions from a source, such as a
file, a database external to server 624, or a database resident in
server 624. Direction parser 684 translates the directions into a
graph. Nodes in the graph represent intersections, and edges
represent the roads connecting the intersections. In one
embodiment, system 620 does not contain a database of roads.
Rather, all the information about the map is obtained from text
directions stored offsite. In another embodiment, server 624
contains direction database 694, which is used to identify a
suitable route between an origin and a destination.
After directions have been parsed by direction parser 684, roads in
the route map are scaled with road layout module 686. In one
embodiment, road layout module 686 applies a constant scale factor
to the entire map so that the map fits in a viewport having
predetermined dimensions. As a result of this uniform scaling, the
map often contains many roads that are too small to see or label.
To remedy this, each road in the map, beginning with the smaller
roads, is scaled by road layout module 686 until roads in the map
are clearly visible. Since the length of roads is only increased in
this step, the map ends up being larger than the size of the
viewport. Thus, in subsequent steps, certain aspects of the map are
reduced to yield a map that fits the dimensions of the desired
viewport.
In one embodiment of the present invention, the size of the map is
reduced by repeatedly initiating a tracing procedure. In this
embodiment, road layout module 686 executes the tracing procedure
until the entire route is traced without identifying a road that
exceeds the dimensions of the viewport. In the tracing procedure,
each successive road in the route is examined, beginning at the
route origin, until a road extending outside the viewport, i.e. an
offending road, is identified. When an offending road is
identified, each road that had been traced is examined to see if it
is capable of being shortened. A road candidate is capable of being
shortened if it is (i) longer than a specified minimum length, (ii)
the relative ordering of the roads by length remains fixed even
after the candidate has been shortened, and (iii) false
intersections are avoided. In one aspect of this embodiment, road
layout module 686 shortens road candidates using a greedy approach
so that the candidate is shortened as much as possible, in order
from longest to shortest, until the offending road is pulled back
inside the viewport.
Label layout module 688 is used to place labels on the scaled map
produced by road layout module 686. To date, proper labeling of
individual roads has been an intractable problem. Label layout
module 688 solves this problem by refining a novel target function
using a simulated annealing schedule. Simulated annealing has been
used to refine label positions in prior art methods. Edmondson et
al., Cartographica 33, 1997, 12 23. However, unlike Edmondson,
which uses a limited set of discrete label positions, the present
invention considers a continuous range of positions for label
placement, and label placements are not limited to positions that
are directly above or below the road. Furthermore, the present
invention uses a more comprehensive target function that considers
the number of roads each label intersects, the number of labels
each label intersects, the distance the label is from the center of
the road associated with the label, and whether the label is above
or below the associated road. Finally, the present invention is
advantageous because roads are extended when the label
corresponding to the road is lengthy.
Annotation module 690 adds decorations, such as road extensions, to
the route map of the present invention. Further, module 690 adds an
icon for route start and end points. Road extensions accentuate
reorientation points, and allow for a larger range of label
positions to be considered. In this phase, all roads are extended
by a small fixed amount. Then only those roads that need to be
extended for the chosen labeling pattern are further lengthened.
FIG. 10 illustrates the advantages of applying road extensions. In
FIG. 10, 1002 represents a road map prior to road extension whereas
1004 represents the same road map after road extension. Labels now
fit the corresponding roads and the map is easier to read.
Geographic and/or commercial context information are added to the
route map by annotation module 690 to help guide the user through
the desired route. In one embodiment, such context information is
obtained from context database 696.
Map renderer module 692 renders the scaled route map. In this
phase, a "sketchy" pen-and-ink style is applied to each road in the
route map. That is, instead of drawing roads as straight lines,
variation is introduced in the bend and width of each road to
generate a hand-drawn look. In an approach similar to that of
Markosian et al., SIGGRAPH 97 Conference Proceedings, 1997, 415
420, each road is broken into small segments and the position of
each point is slightly shifted both normal and tangent to the
segment direction. These points are then joined with a non-uniform
rational b-spline (NURB) to create the final stroke. A NURB is a
curve that interpolates data. Thus, given a set of points, a curve
is generated passing through all the points. The thickness of the
roads is then adjusted to emphasize the route and de-emphasize road
extensions generated by annotation module 690.
Now that an overview of one embodiment of the invention has been
disclosed, a number of advantages of the present inventions are
apparent. First, the present invention discloses a method for
automatically generating a route map that has the clarity of a
hand-drawn map. Such a map is produced by using a novel scaling
function in which each road is scaled individually using the design
criteria of the present invention. Further, a novel method for
positioning labels on the map is disclosed. The refined label
positions help provide a route map having improved clarity.
Map Scaling
Attention now turns to detailed embodiments of road layout module
686. The present invention contemplates several different
implementations of road layout module 686. The different road
layout module embodiments contemplated by the present invention
include but are not limited to uniform scaling, fixed non-uniform
scaling, as well as refinement of individual scale factors using a
greedy search or simulated annealing schedule.
In uniform scaling embodiments, a single scale factor that allows
the graph created by direction parser 684 to fit in a desired
viewport is computed. For viewports that are defined as an x by y
pixel array, a single scale factor, pixelsPerMile, is computed by
an assignment such as:
pixelsPerMile=ComputePixelsPerMile( );
in which the function ComputePixelsPerMile( ) determines the
maximum number of pixels a mile of the route may have without
causing the overall route to exceed the desired pixel-based
viewport. One of skill in the art will appreciate that a single
scale factor for viewports that are based on metrics other than
pixels can be computed using functions analogous to
ComputePixelsPerMile( ). Once a uniform scale factor has been
identified by a function such as ComputePixelsPerMile( ), the
uniform scale factor is applied to the length of each road, and
intersection points between consecutive pairs of roads are updated
to reflect the change in length of the roads. For pixel-based
viewports, the application of the uniform scale factor to each road
reduces to a conversion of miles to pixels. Thus, in such
embodiments, the application of the constant scale factor to each
road takes the form
TABLE-US-00001 (101) for each Road r { (102) r.lengthPxls =
r.lengthMiles*pixelsPerMile; (103) } (104) SetRoadIntersectionPts(
);
In fixed non-uniform scaling embodiments, road layout module 686
includes a rescaleByBucket( ) function that breaks the range of
road lengths (0, infinity) found in the route into N consecutive
buckets [0, x.sub..1), [x.sub.1, x.sub.2), . . . [x.sub.N-1,
x.sub.N), [x.sub.N, infinity). The function then scales the roads
differently depending on which bucket they fall in. Small roads,
those in the earlier buckets, are scaled to be longer, while longer
roads are scaled to be shorter. In one embodiment, roads falling in
the final bucket are capped at some maximum length. In another
embodiment, roads falling in the first bucket are not allowed to
fall below a minimum length. In yet another embodiment, the scale
factor that is chosen for each bucket is subject to the constraint
that the relative ordering of the roads by length remains fixed. In
embodiments in which the route is to be scaled to a pixel-based
viewport, each road is scaled by the uniform scale factor computed
by the ComputePixelsPerMile( ) function described in the uniform
scaling embodiment. Thus, one implementation in accordance with the
non-uniform scaling embodiment, has the steps:
TABLE-US-00002 (201) LayoutRoads( ) (202) { (203) for each Road r {
(204) r.lengthMiles = rescaleByBucket(r.lengthMiles- ); (205)
r.lengthPxls = r.lengthMiles*pixelsPerMile; (206) } (207)
SetRoadIntersectionPts( ); (208) }
Attention now turns to FIG. 7 which illustrates an embodiment of
the present invention in which road layout module 686 refines the
length of roads in the map using a greedy search algorithm. In
processing step 702, road layout module 686 first computes a pixel
to mile conversion factor and applies this factor to each road in
the map so that the map fits into the desired viewport. Then, in
processing step 704, the roads are sorted by length. The relative
order of the roads, in terms of length, in the map as determined in
processing step 704 is maintained throughout the remainder of the
processing steps illustrated in FIG. 7. In some embodiments
deviations in this relative ordering is allowed upon payment of a
penalty. In processing step 706, all small roads are grown until
each road is longer than a set minimum length. Because processing
step 706 only lengthens roads, the route map is not likely to fit
in the desired viewport after processing step 706 has been
executed.
To reduce the map so that it fits into the desired viewport, a
search for roads that can be shortened is performed. In processing
step 708, the route is traversed from the route origin. Each route
in the road is examined (710 714) until a road that extends outside
the viewport (offending road) is identified. When such a road is
identified (710--Yes), a list of candidate roads in the portion of
the route that had been traversed prior to identifying the
offending road is collected (720). To qualify as a candidate road,
a traversed road must be capable of being shortened without
changing the relative ordering of the roads by length and without
falling below a minimum road length. Further, a candidate road must
be capable of being shortened without creating any false
intersections between roads. Finally, the candidate road should be
oriented within .+-.90 degrees of the offending road. Once a road
candidate set has been generated, it is ordered by length, from
longest to shortest (722).
Once the candidate roads have been ordered, a shortening process is
initiated. The shortening process takes advantage of the
computational efficiency of a greedy algorithm to shorten the roads
(724). The shortening process cycles through each candidate road in
the ordered set of candidate roads and shortens the candidate as
much as possible (726) before advancing to the next candidate in
the ordered set (732). After the greedy algorithm is applied to a
candidate road, a check is made to see if the offending road has
been pulled back inside the viewport (728). If the offending road
has been pulled back into the viewport (728--No), the shortening
process ends and control returns to processing step 708.
When the greedy algorithm has been applied to each candidate road
in the ordered set without successfully pulling the offending road
into the viewport (730--Yes), the shortening process repeats the
process of applying the greedy algorithm to each road in the
candidate list (724) until the offending road is pulled back into
the viewport (728--No). The process in FIG. 7 continues until the
complete route can be traversed without identifying a road that
exceeds the dimensions of the viewport (714--Yes, 780). If such a
traversal fails, the shortening process of steps 720 732 is
executed and a new attempt to traverse the route is initiated
708.
At times, an identified road that matches the candidate
requirements indicated above will not be added to the road
candidate set because there is some other road in the route that is
the same length. Roads that have the same length as the identified
road are termed blocking roads. If there is a blocking road, the
identified road cannot be added to the road candidate set because,
if it were shortened, the relative ordering of roads by length, as
identified in processing step 704, would be destroyed. The
occurrence of blocking roads is of interest because, in some
circumstances, they prevent the processing steps of 724 732 from
pulling the offending road into the viewport (728--No). In some
embodiments, when a certain number of iterations of processing
steps 724 through 732 fail to effect a solution (728--No) one or
more of the blocking roads are shortened using the greedy algorithm
discussed previously. Then, if the offending road still exceeds the
dimensions of the viewport, a new road candidate set is generated
(720) and processing steps 724 through 732 are executed until the
offending road no longer exceeds the dimensions of the viewport
(728--No).
FIG. 8 illustrates another embodiment of road layout module 686 in
which the length of roads in the map are refined with a simulated
annealing schedule. In processing step 802, a single scale factor
is applied to each road in the route map. In one embodiment, which
is in accordance with this aspect of the invention, the scale
factor is used to size the map produced by direction parser 684 so
that it fits within the dimensions of the desired viewport. In
another embodiment, the map is sized so that each road in the map
is longer than a selected minimum length so that each road in the
map is legible in the desired viewport.
In the second phase of processing step 802, an initial parameter t
is chosen. The use of a parameter t to obtain better heuristic
solutions to a combinatorial optimization problem has it roots in
the work of Kirkpatrick et al., Science 220, 4598, (1983).
Kirkpatrick et al. noted the methods used to find the low-energy
state of a material, in which a single crystal of the material is
first melted by raising the temperature of the material. Then, the
temperature of the material is slowly lowered in the vicinity of
the freezing point of the material. In this way, the true
low-energy state of the material, rather than some high
energy-state such as a glass, is determined. Kirkpatrick et al.
noted that the methods for finding the low-energy state of a
material can be applied to other combinatorial optimization
problems if a proper analogy to temperature as well as an
appropriate probablistic function, which is driven by the this
analogy to temperature, can be developed. The art has termed the
analogy to temperature an effective temperature. Therefore,
parameter t will henceforth be termed an effective temperature. It
will be appreciated that any effective temperature t may be chosen
in processing step 802. One of skill in the art will further
appreciate that the refinement of an objective function using
simulated annealing is most effective when high effective
temperatures are chosen. There is no requirement that the effective
temperature adhere to any physical dimension such as degrees
Celcius, etc. Indeed, the dimensions of the effective temperature t
used in the simulated annealing schedule adopts the same units as
the objective function that is the subject of the optimization.
In one embodiment, a starting effective temperature that is readily
reduced by ten percent on a periodic basis is chosen, such as
1.0/log(3)*3. In another embodiment, the starting value of t is
based on a function of one or more of the characteristics of the
route to be scaled, such as the number of roads in the route, the
number of intersections in the route, and/or the length of the
route. In another embodiment, the starting value of t is selected
based on the amount of resources available to compute the simulated
annealing schedule. For example, the starting value of t is reduced
below a pre-specified default value when the annealing schedule is
to be run on a server that is currently refining several other
routes or on a relatively slower client. In still another
embodiment, the starting value of t is related to the form of the
probability function used in processing step 814. It has been
found, in fact, that the effective temperature does not have to be
very large to produce a substantial probability of keeping a worse
score. Therefore, in some embodiments, starting effective
temperature t is not large.
Once a single scale factor has been applied to each road in the
route map and an initial starting effective temperature has been
assigned, an iterative process begins. A counter is initialized in
processing step 804 and, in processing step 806, the quality of the
map (E.sub.1) is assessed using an objective function. It will be
appreciated that the utility of the map produced by the simulated
annealing schedule is dependent upon the development of an
objective function that accurately balances the various features of
the map that need to be optimized. In one embodiment, the objective
function is dependent upon the number of false intersections each
road in the route makes, the number of roads in the route that no
longer have the same relative length that they had before the
simulated annealing schedule was initiated, and the number of roads
that fall below a minimum length. An objective function in
accordance with this embodiment is:
E=[.sub.i=1.SIGMA..sup.Nw.sub.1*false_intersection.sub.i]+[w.sub.2*Num_w/-
o_rel_len]+[w.sub.3*num_short_roads] where, w.sub.1, w.sub.2 and
w.sub.3 are independently selected weights; false_intersection, is
the number of false intersections road i makes; N is the number of
roads in the route; num_w/o_rel_len is the number of roads that no
longer have the same relative length that they had before simulated
annealing schedule was initiated; and num_short_roads is the number
of roads that are shorter than a minimum length threshold.
After the quality (E.sub.1) of the map has been measured using the
objective function, a scale factor is randomly generated and
applied to a randomly selected road (808). In one embodiment, the
scale factor is randomly chosen from a permissible range, such as
zero to two. Thus, in such an embodiment, a random number generator
is used to identify a number in the range zero to two, such as
"0.6893." The random number is then applied to a randomly selected
road in the route as a scale constant. For example, if the number
is "0.6893" and the randomly selected road is the j.sup.th road in
the route map, the j.sup.th road is shortened by 31.07 percent. In
another embodiment, the permissible range for the random number is
-0.1 to 0.1 and therefore, in such embodiments, application of the
randomly chosen scale constant is capable of altering the length of
the j.sup.th road by no more than ten percent.
After the length of the j.sup.th road has been adjusted by the
scale factor, the quality of the map (E.sub.2) is calculated using
the same objective function used in processing step 806 (810). When
the quality of the map has improved (E.sub.2<E.sub.1)
(812--Yes), then the change made to the length of the j.sup.th road
is accepted (830). When the quality of the map has not improved
(E.sub.2>E.sub.1) (812--No) the change made to the length of the
j.sup.th road is accepted with the probability:
1-exp.sup.-[(.DELTA.E)/k*t)] (1)
From the form of equation (1), it will be appreciated that the
probability that the change is accepted, when (E.sub.2>E.sub.1),
is lower at lower effective temperatures t. Equation (1) is
implemented as processing steps 814 through 818 in FIG. 8. In
processing step 814, exp.sup.-[(.DELTA.E)/k*t)] is computed. In
processing step 816, a number P.sub.ran in the interval 0 to 1 is
generated. If P.sub.ran is less than exp.sup.-[(.DELTA.E)/k*t)]
(818--Yes), the change made to the j.sup.th road in processing step
808 is accepted (830). If P.sub.ran is more than
exp.sup.-[(.DELTA.E)/k*t)] (818--No), the change made to the
j.sup.th road in processing step 808 is rejected (840). It will be
appreciated that probability functions other than that disclosed in
equation (1) are within the scope of the present invention.
Acceptance of conditions (E.sub.2>E.sub.1) on a limited
probabilistic basis is advantageous because it provides the
refinement system with the capability of escaping local minima
traps that do not represent a global solution to the objective
function. One of skill in the art will appreciate, therefore, that
probability functions other than that of equation (1) will advance
the goals of the present invention. Representative probability
functions include, for example, functions that are linearly or
logarithmically dependent upon effective temperature, rather than
exponentially dependent on effective temperature as described in
equation (1).
Processing steps 806 through 840 represent one iteration in the
refinement process. In processing step 842 an iteration count is
advanced. When the iteration count does not exceed the maximum
iteration count, the process continues at step 806 (844--No). When
the iteration count equals a maximum iteration flag (844--Yes),
effective temperature t is reduced (846). One of skill in the art
will appreciate that there are many different types of schedules
that are used to reduce effective temperature t in various
embodiments of processing step 846. All such schedules are within
the scope of the present invention. In one embodiment, effective
temperature t is reduced by ten percent. In another embodiment,
effective temperature t is reduced by a constant value. For
example, the starting effective temperature set in processing step
802 could be 20,000 and this effective temperature could be reduced
by 300 each time processing step 846 is executed. In another
embodiment the percentage decrease in effective temperature in
processing step 846 is calculated as a function of the number of
roads to be scaled.
When the effective temperature has been reduced by an amount in
processing step 846, a check is performed to determine whether the
simulated annealing schedule should be terminated (848). In the
embodiment illustrated in FIG. 8, the process is terminated
(848--Yes, 850) when effective temperature t has fallen below a low
effective temperature threshold or E.sub.2 falls below a
predetermined low quality threshold. The low effective temperature
threshold is any suitably chosen effective temperature that allows
for a sufficient number of iterations of the refinement cycle at
relatively low effective temperatures. When it is determined that
the annealing schedule should not end (848--No), the process
continues at step 804 with the reinitialization of iteration count
i.
In another embodiment of the present invention, a distinctly
different exit condition than the one illustrated in FIG. 8 is
used. In this alternative embodiment, a separate counter is
maintained. This counter, which could be termed a stage counter, is
incremented each time t is reduced in step 846. When the stage
counter has exceeded a predetermined value, such as fifty, the
simulating annealing process ends (850). In yet another embodiment,
a counter tracks a consecutive number of times the arbitrary scale
factor is rejected (840). When a set number of arbitrary changes in
a row have been rejected, the route map is considered optimized and
the process ends (850).
Map Annotation
In one embodiment, annotation module 690 is used to
deterministically place context information on the map after the
map has been scaled by road layout module 686. In one aspect of
this embodiment, the context information represents points of
geographical interest and helps to guide the user through the route
to the destination. In another embodiment, the context information
represents a form of advertisement that is paid for by subscribers.
In one example in accordance with such embodiments, the subscriber
is a fast food chain and the landmarks represent the location of
each fast food franchise that is associated with the fast food
chain. It will be appreciated that an important advantage of the
present invention is that the route maps do not contain superfluous
content. Thus, the route maps of the present invention are
particularly well suited for use in conjunction with geographical
landmarks that are paid for by subscribers. In one embodiment of
the present invention, memory 668 of server 624 includes a context
database 696 that is populated with context information that has
been provided by and paid for by advertisers.
Label Refinement
Identification of an optimal position for each label in the route
map improves the quality of the map because clutter and object
overlap is reduced. The present invention optimizes label position
by minimizing a novel target function that scores the position of a
label using a unique set of label parameters. Importantly, rather
than considering a small number of discrete positions for label
placement, a continuous range of positions within a region around
the center of the road being labeled are considered. This region
includes positions that are not directly above or below the road
being labeled. When a position that is not directly above or below
the road is selected, the road is extended to the position of the
label.
In one embodiment, the target function is optimized using a
simulated annealing schedule. FIG. 9 illustrates one embodiment in
accordance with the present invention. In processing step 900, each
label is placed at the center of the road corresponding to the
label and an initial effective temperature t is selected. It will
be appreciated that effective temperature it may be set to wide
range of possible effective temperatures in processing step 900. In
one embodiment, a starting effective temperature that is readily
reduced by ten percent on a periodic basis, such as 1.0/log(3)*3,
is chosen. In another embodiment, the starting effective
temperature is based on a function of one or more of the
characteristics of the route to be optimized, such as the number of
labels in the route, the amount of context information along the
route, and/or the length of the route. In another embodiment, the
starting effective temperature is selected based on the amount of
resources available to perform the simulated annealing
calculations. For example, the initial effective temperature is set
to a low value when the annealing schedule is to be run on a server
that is currently refining several other routes or a client with a
relatively slow central processing unit. In still another
embodiment, the starting effective temperature t is determined by
the nature of the probability function that is used to accept
scores having S.sub.2>S.sub.1.
In processing step 902 the stage counter is set to zero. The stage
counter is incremented each time effective temperature t has been
reduced. Once the initialization steps of processing step 900 have
been performed, counter i is set to one (902) and a label j is
randomly selected (904). The quality of the position of the
j.sup.th label (S.sub.1) is measured using a target function, which
is designed to measure label position quality, in processing step
906 and in processing step 908 the j.sup.th label is repositioned
by a random amount. In step 908, the quality of the repositioned
j.sup.th label (S.sub.2) is measured. An important advantage of the
present invention is that the j.sup.th label is repositioned into
any of a continuous range of values rather than a limited number of
discrete positions. Further the target function used to compute
S.sub.1 and S.sub.2 provides an improved method for assessing the
quality of a label position. In one embodiment the target function
includes the following components:
TABLE-US-00003 (301) collect all objects that intersect the
j.sup.th label (302) for each intersecting object { (303) case
ROAD: (304) score += ROAD_PENALTY; (305) case LABEL: (306) score +=
LABEL_PENALTY; (307) case ANNOTATION: (308) score +=
ANNOTATION_PENALTY; }
In line 301, all the objects that intersect the j.sup.th label are
collected. Such objects include, for example, roads, other labels,
and annotations such as context information. The target function
loops through each of the collected objects (line 302). When the
object is a road, a road penalty is added to the score (line 304),
when the object is a label, a label penalty is added to the score
(line 306) and when the object is an annotation, an annotation
penalty is added to the score (line 308).
In some embodiments, the target function includes one or more
additional components. One such component is an off screen penalty.
When the j.sup.th label is positioned such that a portion of the
label exceeds the boundary of the viewport, an off screen penalty
is added to the score. Another component is a "distance from the
center of the corresponding road penalty." This penalty is
determined by taking the product of a centering penalty and the
normalized distance of the j.sup.th label from the road center.
Additional components in the target function represent various
constraints that are imposed on the label position. Constraints are
used to bias label positions that are consistent with label
position design criteria. For example, in one embodiment, it is
preferable to position a label above the road rather than below the
road. Thus, a below_the_road constraint penalty is added to the
score of a label position that is below the road corresponding to
the label. Another constraint penalty asks whether a road should be
extended so that the road runs alongside the label. When it is
determined that a road extension will provide better label to road
correspondence, a road extension penalty is added to the target
function score. Yet another constraint penalty is used when the
label is positioned far away from the center of the corresponding
road. In such cases, an arrow is positioned on the map to indicate
the relationship between the label and the corresponding road and
an arrow penalty is added to the target function.
In one embodiment, the target function has the form:
TABLE-US-00004 (401) float score = 0.0; (402) // Get all the
objects that intersect the label (403) for each object { (404) case
ROAD: (405) score += ROAD_PENALTY; (406) case LABEL: (407) score +=
LABEL_PENALTY; (408) case ANNOTATION: (409) score +=
ANNOTATION_PENALTY; (410) } (411) // Is label completely visible on
viewport? (412) if not { (413) score += OFF_SCREEN_PENALTY; (414) }
(415) score += normalized distance from road center *
CENTERING_PENALTY; (416) score += constraint penalty; (417) return
score;
When the quality of the j.sup.th position has improved
(S.sub.2<S.sub.1) (912--Yes), the new label position for the
j.sup.th label is accepted (930). When the quality of the map has
not improved (S.sub.2>S.sub.1) (912--No) there is a probability
1-exp.sup.-[(.DELTA.S)/k*t)] (2) that the new label position for
the j.sup.th label will be accepted. From the form of equation (2),
it will be appreciated that, for cases in which
(S.sub.2>S.sub.1), the probability that the change in label
position will be accepted diminishes as effective temperature t is
reduced. Equation (2) is implemented as processing steps 914
through 918 in FIG. 9. In processing step 914,
exp.sup.-[(.DELTA.S)k*t)] is computed. In processing step 916, a
number P.sub.ran, in the interval 0 to 1, is generated. If
P.sub.ran is less than exp.sup.-[(.DELTA.S)/k*t)] (918--Yes), the
change made to the j.sup.th label position in processing step 908
is accepted (930). If P.sub.ran is more than
exp.sup.-[(.DELTA.S)/k*t)] (918--No), the change made to the
j.sup.th label position in processing step 908 is rejected (940).
It will be appreciated that probability functions other than the
function shown in equation (2) and processing step 914 are within
the scope of the present invention. Indeed, any probability
function that is dependent upon effective temperature is
suitable.
Processing steps 904 through 940 represent one iteration in the
annealing process. In processing step 942, an iteration count is
advanced. When the iteration count does not exceed the maximum
iteration count (944--No), the process continues at step 904. When
the iteration count equals a maximum iteration flag (944--Yes),
effective temperature t is reduced and the stage counter is
advanced (946). One of skill in the art will appreciate that there
are many possible different types of schedules that are used to
reduce effective temperature t in various implementations of
processing step 946. All such schedules are within the scope of the
present invention. In one embodiment, effective temperature t is
reduced by ten percent each time processing step 946 is executed.
In another embodiment the percentage decrease in effective
temperature t in processing step 946 is calculated as a function of
the number of labels to be scaled. After processing step 946, a
check is performed to determine whether the simulated annealing
schedule should be terminated (948). When it is determined that the
annealing schedule should not end (948--No), the process continues
at step 902 with the re-initialization of iteration count i.
In the embodiment illustrated in FIG. 9, the process is terminated
(948--Yes, 950) when a maximum number of stages has been executed.
In one embodiment, the maximum number of stages executed is fifty.
In embodiments other than that illustrated in FIG. 9, criteria
other than the stage count is used in processing step 948 to
determine when the simulated annealing process should be
terminated. Such criteria include terminating the process when
effective temperature t has fallen below a low effective
temperature threshold, when E.sub.2 or E.sub.1 falls below a
predetermined low quality threshold, or when the consecutive number
of times the new label position has been rejected exceeds a
threshold value.
Map Rendering
The final phase of the process is the rendering of the route by map
renderer module 692. In this phase, the route map is humanized. In
some embodiments, techniques used to humanize the map include
casting the roads in a "sketchy" pen-and-ink style, adding a
breakage symbol to long roads that have been significantly scaled
down by road layout module 686, providing an indication of road
length for long roads in the route, adding an arrow to indicate
which way is North, and/or adding insets that show enhanced route
detail.
Map renderer module 692 produces the "sketchy" style by breaking
each road into small segments and slightly shifting the position of
each segment both normal to the stroke direction and along the
stroke directions. The rotated segments are then joined with a NURB
to create the final stroke. Further, the thickness of the roads is
adjusted to emphasize the route and de-emphasize route extensions.
In a preferred embodiment, a hand-drawn font is used for the
labels.
Overview of Alternative Embodiments for Abstracting and Visualizing
Route Maps
Embodiments for producing scaled route maps have now been described
in detail. In the following sections, details of alternative
embodiments for scaling route maps are provided. Full appreciation
of these alternative embodiments is best obtained by first
providing an overview of the basic processing steps performed by
these alternative embodiments.
Obtain route directions. First, directions are obtained by
direction parser 684 from a source such as direction database 694
(FIG. 6). Although direction database is depicted as being on the
same server 624 as direction parser 684, it will be appreciated
that there is no requirement that direction database 694 reside on
the same server. Indeed, direction database 694 may take several
different forms and reside at any address that is in communication
with transmission channel 626.
Road simplification. Once road directions are obtained, an initial
route map is constructed. Then, as will be described in further
detail below, a pass is made by road shape simplification module
697 at simplifying the initial route map. If successful, road shape
simplification module 697 removes one or more shape points from
some of the roads in the route map, thereby reducing the complexity
of the route map without sacrificing map legibility and utility.
Furthermore, the reduced complexity of a simplified route map
facilitates computationally intensive map refinement and scaling
that arises in subsequent processing stages.
Map page design. In the map page design stage, the dimensions of
the viewport that the map will be displayed in or printed onto are
considered. A layout template is chosen by road layout module 686
based on the dimensions of the viewport. Furthermore, the route map
is optionally rotated by map verticalization module 698 in order to
optimize the dimensions of the route map to the dimensions of the
viewport. When the route map includes several steps, map division
module 699 is invoked in order to break the route map into a
plurality of segment maps in a manner that is consistent with the
selected layout template.
Road layout. At this stage, road layout module 686 scales each road
independently (i.e. nonuniformly). The nonuniform scaling is driven
by an optimization algorithm such as simulated annealing in order
to achieve a suitable scaled map. The target function used by the
optimization algorithm utilizes a novel scoring strategy that is
designed to quantify map scale quality.
Label layout. Once the map has been scaled, the route map is
populated with road labels by label layout module 688. Each label
is associated with a constraint definition that defines the
boundaries in which the label may be placed and the format of the
label. Using these constraint definitions, label layout module 688
refines the label locations using an optimization algorithm having
a target function that quantifies label position quality.
Map Annotation. Cross streets, land marks and an optional North
arrow are added to the map during the map annotation stage.
Annotation module 690 identifies suitable landmarks that will
assist the navigator while using the route map. Such landmarks may
be derived from a source such as context database 696. It will be
appreciated that annotation module 690 can be used in some
embodiments for commercial benefit. For example, licensing schemes
are envisioned in which a retailer pays to have the location of
each franchise positioned on the map as landmarks.
Map rendering. Other stages of the map scaling process considered
the route map in an abstract sense. In the map rendering stage, the
components of the route map, including the main route, cross
streets, landmarks, and the North arrow are reduced from an
abstract sense to an actual image. In one embodiment, this image is
a pixel based image. The stage of the process is performed by map
renderer module 692.
Now that an overview of this series of alternative embodiments have
been provided, novel aspects of the series of embodiments will be
examined in detail.
Alternative Scoring Functions Used in Road Layout Refinement
As outlined in the overview, an important aspect of the map scaling
process is performed by road layout module 686. Road layout module
686 scales each road in a route map in a nonuniform manner. In
embodiments in which road layout module 686 includes a simulated
annealing schedule the following steps are performed:
1. Generate an initial road layout by growing all short roads to a
desired minimum length.
2. Obtain an initial score E for the initial road layout using an
objective function and set an initial effective temperature.
3. While E is greater than an acceptable score, the number of
iterations is less than the maximum allowed iterations, and the
effective temperature is above some lower threshold level, repeat
steps four to eight.
4. Choose a random road and grow or shrink it by a random amount;
re-scale all roads so they fit inside the viewport.
5. Obtain a new score E for the new road layout generated in step
four.
6. If new score E is less than initial score E, accept the new road
layout generated in step four.
7. If new score E is greater than initial score E, accept the new
road layout in accordance with some decreasing probability, in
order to escape local minima.
8. Adjust effective temperature.
It will be appreciated that the simulated annealing protocol
outlined above and described in detail in FIG. 8 is not limited to
any specific scoring function. Indeed, various embodiments of road
layout module 686 use a wide array of scoring functions to
determine the initial score E.sub.1 (806 FIG. 8) as well as new
scores E.sub.2 (810 FIG. 8). Applicants have described an objective
function in accordance with one embodiment of road layout module
686 that is determined by (i) the number of false intersections
made be each road i in a route map, (ii) the number of roads that
no longer have the same relative length that they had before
simulated annealing schedule was initiated, and (iii) the number of
roads that are shorter than a minimum length threshold.
In another embodiment of road layout module 686, processing steps
806 and 810 in FIG. 8 use a scoring function represented by the
following representative code.
TABLE-US-00005 (501) Score( ) (502) Score = 0.0; (503) Score +=
IntersectionScore( ) (504) Score += ShuffleScore( ) (505) Score +=
RoadLengthScore( ) (506) Score += RatioScore( ) (507) Score +=
EndPointDirectionScore( ) (508) Score += EndPointDistanceScore(
)
Each subscore considers a specific aspect of the road layout, and
are prioritized as follows:
Highest Priority
Intersections: maintaining existing intersections and not
introducing false intersections.
Road length: scaling all roads to be readable.
Shuffles: maintaining relative lengths of the roads.
End Point Direction: maintaining overall orientation of route.
Ratios: maintaining ratios in lengths between roads.
Lowest Priority
End Point Distance: maintaining distance between start and
destination points of the route.
In this embodiment, the scoring function used by road layout module
686 assigns higher priority to the aspects of the road layout that
are most important to resolve. For example, a map with missing
and/or false intersections can be misleading. On the other hand,
maintaining overall distance and orientation of the route is useful
but not required for a navigator to follow the route. Thus,
resolving intersections is given a higher priority than maintaining
end point distance in this embodiment of road layout module
686.
Line 502 of the representative code initializes the variable
"Score" to zero. The variable "Score" represents E.sub.1 (806 FIG.
8) or E.sub.2 (810). Next, lines 503 through 508 each potentially
add to the value of "Score." Higher values of score represent
higher values for E.sub.1 and E.sub.2 and thus represent poor
solutions. Each of the functions that contribute to the overall
value of "Score" on lines 503 through 508 is discussed with more
detail below.
IntersectionScore( ). The first function to contribute to the
variable "Score" in the representative code is function
"IntersectionScore( )" on line 503. Maintaining proper
intersections between roads is the highest priority in the
disclosed scoring function. In the initialization of the annealing,
all of the roads in the route map are grown to their desired
minimum lengths. Growing the roads can lead to two problems:
intersections may be introduced between roads that should not
intersect (false intersections), or two roads that should intersect
no longer intersect (missing intersections). FIG. 40 illustrates
both of these scenarios. FIGS. 40A and 40C each represent an
original map whereas FIGS. 40B and 40D represent perturbed maps.
FIG. 40B represents a situation in which a false intersection 4002
arises. FIG. 40D represents a situation where a missing
intersection 4004 arises. Both missing and false intersections can
be extremely misleading and therefore are severely penalized in any
proposed layout that has either of these problems.
The role of the scoring function in road layout module 686 is to
guide the layout algorithm to the desired layout. One approach to
furthering this goal is to add a fixed constant penalty when either
of these conditions exists. However, this scoring function does not
provide adequate guidance because the same penalty is always added
to the score no matter how severe the false or missing
intersection. Suppose the route contains a missing intersection as
shown by 4004 in FIG. 40D. If the layout is perturbed and the
missing intersection points end up closer to one another but do not
exactly match, the intersection score for this map will not change.
The algorithm will not know that moving the missing intersection
points closer together generates a better layout. In other words
the annealing algorithm is less likely to converge. Thus, in this
embodiment, a score is constructed that reflects the severity of
the intersection problems in a manner that suggests how they might
be resolved rather than using a constant penalty for each false or
missing intersection. What follows is a description of how simple
false and missing intersections are resolved independently by the
disclosed scoring function. Next, a description is provided for how
scoring must change when there are both false and missing
intersections in a single map.
Missing and Misplaced Intersections. If two roads should intersect
but don't (missing intersection), a factor is added to the score
that is related to the distance between the proper intersection
point on each road. The proper intersection point is computed from
the parametric value of the original intersection in the unscaled
map. If the roads should intersect and do intersect but at the
wrong point (misplaced intersection), a factor is also added that
is related to the distance between the proper intersection point on
each road. The scoring weight for a misplaced intersection is much
less than for a missing intersection. This score is illustrated in
FIG. 41. FIG. 41A represents how a missing intersection is scored
whereas FIG. 41B represents how a misplaced intersection is scored.
The general formulas for computing the intersections are:
missingscore=d*MISSING_SCORE_WEIGHT
misplacedscore=d*MISPLACED_SCORE_WEIGHT
where d is the Euclidian distance between the two points that
should intersect as represented in FIG. 41.
Simple False Intersections. False intersections occur when the path
incorrectly folds back on itself, forming a loop or knot. To remove
false intersections, the knot must be unraveled. To remove any
individual knot it is desirable to make the false intersection
point move toward the closest endpoint (in pixels along the route)
of the path (or similarly, make the closest endpoint move towards
the false intersection point). FIG. 42 illustrates several false
intersection scenarios, showing for each false intersection point
which direction the closest endpoint must travel to remove the knot
formed by that false intersection point. FIG. 42A represents the
simplest case, one false intersection 4202. End point 4204 simply
needs to move to the right to resolve the false intersection. FIGS.
42B and 42C show which direction endpoints should move to resolve
each false intersection point independently. FIG. 42B represents a
situation in which multiple false intersection points 4208 are near
the same endpoint 4206. The two false intersection points 4208 are
pulling endpoint 4206 in opposing directions. FIG. 42C represents
the case of multiple false intersection points (4214, 4216) that
are near different endpoints (4210, 4212). In this case, false
intersection points 4214 and 4216 are entirely independent of each
other.
Computing the score for an individual false intersection point is
relatively straightforward. It is desirable to move the false
intersection point towards the closer endpoint of the route, or
alternatively to move the closer endpoint towards the false
intersection point. FIG. 43 illustrates a knot that is produced by
false intersection 4302. One way to resolve false intersection
4302, is to push the endpoint that is closer to false intersection
4302 towards the false intersection. To determine which endpoint
(4304 or 4306) is closer to false intersection 4302, the distance
between each endpoint and the false intersection is computed and
compared. Then, the endpoint that is closer to the false
intersection is moved towards the false intersection.
Viewing each false intersection independently, the score for each
false intersection point is computed as the "distance in pixels
along the route to the nearest end point" multiplied by a scoring
weight. This is equivalent to conceptually building a scoring hill
along the route that guides the false intersection point to the
closer endpoint, where it can be removed. Therefore, the score for
a single false intersection can be computed as:
falsescore=d*FALSE_SCORE_WEIGHT where d is the distance in pixels
to the endpoint along the route, as opposed to straight line
distance, as shown in FIG. 43. However, as illustrated by the
scenario in FIG. 42B, if the score for each false intersection is
computed this way, then when there are multiple false intersections
the scores will push the endpoint in opposite directions. However,
this problem is addressed by always counting only the score for the
innermost false intersection (i.e. the one farthest from the
endpoint). The difference between counting all false intersections
and only the innermost false intersection is shown in FIG. 44. FIG.
44A illustrates the situation in which, if the scores for both
false intersections 4404 are counted, endpoint 4402 is pulled
equally in both directions, resulting in a plateau in the scoring
function since a move of endpoint 4402 in either direction does not
change the score. FIG. 44B illustrates the situation in which only
the innermost false intersection is counted for each endpoint. In
the situation described in FIG. 44B, once the innermost false
intersection has been resolved, the remaining false intersection
becomes the innermost false intersection and is subsequently
resolved. In situations such as FIG. 42C, where there are two false
intersections but they are both closer to different endpoints, both
scores are counted against these respective endpoints.
False Intersections and Missing Intersections In general, when both
false and missing intersections occur in the same map they can be
scored as previously described, and in most cases the scores will
interact properly to resolve both problems. However, there is one
exceptional situation. This situation occurs when a missing
intersection occurs within the loop formed by a false intersection.
Several variations of this situation are illustrated in FIG. 45. In
FIG. 45A, one point 4502 of the missing intersection is within the
loop formed by a false intersection 4504. In FIG. 45B, both points
4506 are within the loop formed by false intersection 4508. In both
of the situations shown in FIG. 45, one score may push in one
direction and the other score in the other direction, resulting in
a stalemate in which neither problem can be resolved. FIG. 46 shows
the same routes as FIG. 45, but with arrows 4610 added to indicate
the direction that the two scores would move the endpoints 4602 and
4604.
An important point to note about the situations arising in FIG. 45
is that resolving the missing intersection often resolves the false
intersection. In FIG. 45, there is supposed to be an intersection,
it is just occurring between the wrong roads. It is quite often the
case when a missing intersection occurs within the loop of a false
intersection that the false intersection is simply the missing
intersection misplaced. This situation is resolved with one
additional rule: if there is some point of a missing intersection
inside the loop formed by a false intersection a constant penalty
is added for the false intersection, not a hill-based score. Thus,
both of the cases that are shown in FIG. 45 will use a constant
penalty for the false intersection, as both contain at least one
point of a missing intersection within the false intersection
loop.
With this introduction an algorithm for scoring missing and false
intersections can now be stated with lines 601 through 633 of the
illustrative code.
TABLE-US-00006 (601) void score_false_intersection(Road* self,
Road* other) { (602) if (missing_intersection_in_loop) { (603) //
false intersection loop contains a missing intersection (604) if
(closest_to_route_endpoint(self,other)) { (605)
self->IncrementScore (FALSE_INTERSECTION_CNST); (606) } else {
(607) // no missing intersection in loop (608) if
(closest_to_route_endpoint(self,other)) { (609)
self->IncrementScore(pixelsToClosestEndpoint * (610)
FALSE_INTERSECTION_HILL); (611) // Compute the max possible
extended intersection (612) // score. All false intersection scores
must be increased (613) // by the max extended intersection score
to ensure that (614) // there is no valley between solving all the
false inter- (615) // sections and introducing the extended
intersections. (616) self->IncrementScore(MaxExtendedI-
ntersectionScore); (617) } } } (618) void
ScoreMissingIntersection(Road* self, Road* other) { (619) double
missingIntersectionScore = 0.0; (620) // We know where the two
roads should have intersected (621) // in terms of T values along
each road. Compute distance // between these two points. (622) for
(each missing intersection between self and other) { (623) double
dist = (ptSelf - ptOther).length( ); (624) // Before the roads
touch use a higher penalty. After they (625) // touch reduce the
penalty constant to make sure that the (626) // anneal will
maintain the touch. (627) if (no intersection between self and
other) { (628) double missingScore = dist * MISSING_INTERSECTION;
(629) self->IncrementScore(Road::INTERSEC- T, missingScore);
(630) } else { (631) self->IncrementScore(Road::INTERSECT, dist
* (632) MISPLACED_INTERSECTION); (633) } } }
Examining lines 601 through 633 of the illustrative pseudo-code in
detail, one will notice that an additional score,
"MaxExtendedIntersectio-nScore" is added to the false intersection
scores. This function is described below in conjunction with an
explanation of the concept of extended intersections.
Extended Intersections. In addition to avoiding actual
intersections between roads, it is desirable to avoid having roads
pass close enough to each other that they appear to touch. These
situations are handled in one embodiment of road layout module 686
by using the concept of an extended intersection. Extended
intersections between two roads are calculated by extending both
endpoints of each road by a fixed number of pixels and then
checking if the resulting roads intersect. This concept is
illustrated in FIG. 47. In particular, in FIG. 47A, the roads do
not actually intersect but are close to one another. In FIG. 47B,
when the roads are extended by a fixed number of pixels, the roads
do intersect. If an extended intersection does occur between two
roads it is scored in the following manner for each of the two
roads:
(a) if the intersection occurs in the extended part of the road, as
for road 4702 in FIG. 47A, then the number of pixels from the end
of the extended road is computed and multiplied by a fixed
constant.
(b) if the intersection occurs within the unextended portion of the
road, as for road 4704 in FIG. 47A, then a fixed constant, which is
equal to the largest penalty that can be assigned for an
intersection with the extended portion of the road, is added to the
score.
There is one complication with handling extended intersections.
When trying to resolve a false intersection, extended intersections
often cause many local minimums in the search space. This is
illustrated in FIG. 48, where an extended intersection 4802 works
against the resolution of false intersection 4804. To reduce the
number of local minimums in the search space explored by the target
function as much as possible, only extended intersections are
counted towards the score when they are not likely to be
counteracting the resolution of a false intersection.
Implementation of this criteria requires two things:
(a) knowing when to, and when not to, count an extended
intersection towards the score, and
(b) adding the largest possible extended intersection score to the
base false intersection score. Otherwise, when a false intersection
is resolved the target function starts counting a number of
extended intersections, and their increased score may overwhelm the
decrease in score from resolving the false intersection. This may
cause a substantial local minimum in the search space that would
prevent the resolution of most false intersections. However, in a
preferred embodiment road layout module 686, the maximum extended
intersection score is added to each false intersection score. This
guarantees that the resolution of a false intersection will result
in a decrease in score.
A way to determine which extended intersections to add to the score
is to divide the route into false intersection intervals. All roads
between an endpoint of the map and a false intersection, or between
a pair of false intersections are considered to be in the same
false intersection interval. This concept is illustrated in FIG.
49. In FIG. 49, the same route shown in FIG. 48 is illustrated, but
the route is segmented by false intersection intervals. In
particular, there are three false intersection intervals in FIG.
49: (A) from start point 4802 up to, but not including, the first
road with a false intersection, (BCDE) which is from the road with
a false intersection up to the next road with a false intersection,
and (FGH) which is from the last false intersection to the
endpoint. Extended intersections are only counted between roads in
the same false intersection interval. Thus, the extended
intersection shown in FIG. 48 would not be counted. If only
extended intersections that occur between roads in the same false
intersection intervals are added, then the problem depicted in FIG.
48 will not occur.
ShuffleScore( ). The second function to contribute to the variable
"Score" in the representative code is function "ShuffleScore( )" on
line 504. The purpose "ShuffleScore( )" is to maintain the relative
lengths of the different roads in the scaled route map the same as
they were in the unscaled route map. In function "ShuffleScore( ),"
for each pair of roads A and B in the route map, the ordering of
the roads by length in the scaled map is compared with the ordering
of the roads by length in the original unscaled map. If the
ordering has changed, roads A and B are considered shuffled and a
factor is added to the variable "Score" to reflect this. In one
embodiment, however, roads are only considered shuffled when their
difference in lengths is greater than some perceptual threshold.
Typically, the perceptual threshold used is dependent upon the
resolution and size of the viewport that is used to visualize the
route map as well as factors such as whether the full scaled route
map is being displayed in the viewport as opposed to a scaled up
segment of the scaled route map. The purpose of the penalty applied
by function "ShuffleScore( )" is to ensure that, whenever possible,
the relative ordering of roads by length is maintained in the
scaled route map.
In one representative target function used by an embodiment of road
layout module 686, "ShuffleScore( )" is represented by the
following expression:
For each pair of roads (A, B) Compare the ordering of the roads by
length in the current map with the ordering of the roads by length
in the original map. If the ordering has changed then add a
constant penalty to the score to reflect this. Roads are only
considered shuffled when their difference in lengths is greater
than some perceptual threshold.
RoadLengthScore( ). The overall goal of the non-uniform scaling of
maps that is implemented by road layout module 686 is to make all
of the roads in the route large enough to be legible. This is
tracked by the third function ("RoadLengthScore( )"), which
contributes to the variable "Score", as found on line 505 of the
representative code. In function "RoadLengthScore( )," the current
length of each road in the route map is compared to a predetermined
minimum desired length. If a road is less than the minimum desired
length, then a factor is added to the variable "Score." The
magnitude of this factor is a function of the power of the
difference between the current length of the offending road and a
predetermined minimum acceptable road length. The predetermined
minimum acceptable road length is set to ensure that the road is
long enough to be identifiable in the scaled route map. In some
embodiments of the present invention, the predetermined minimum
acceptable road length is designated by considering the dimensions
of the viewport 640 (FIG. 6) used to display the scaled route map
or the number of pixels in viewport 640. In one example, when
viewport 640 is a 1024 by 768 pixel array, the predetermined
minimum acceptable road length is 20 pixels. In another example,
the predetermined minimum acceptable road length is set to four
percent of the length of the shortest dimension of viewport 640.
Thus, if viewport 640 has a display that is 5 by 6 centimeters, the
predetermined minimum acceptable road length is set to 0.2
centimeters.
In one representative target function used by an embodiment of road
layout module 686, "RoadLengthScore( )" is represented by the
following expression:
For each road (A) Compare the current length to a predetermined
minimum desired length. If less than the minimum desired length
then add a factor to the score. The factor is related to a power of
the difference between the current length and the desired minimum
length. The minimum desired length is set to ensure the road is
long enough to be perceived and labeled and that the relative
lengths are preserved.
RatioScore( ). The fourth function to contribute to the variable
"Score" is function "RatioScore( )," which is on line 506 of the
representative code. One of the lowest priority contributors to
"Score," function "RatioScore( )" is used to maintain the ratios
between different road lengths. Function "RatioScore( )" examines
each road A in the scaled route map whose length is greater than
the predetermined minimum acceptable road length described in the
discussion of function "RoadLengthScore( )" above. For each such
road A in the scaled route map, the ratio of the length of the road
is compared to the next shorter and next longer road in the route
map. The ratios obtained from these comparisons is matched with the
corresponding ratios obtained from the unscaled route map. When the
ratio between road A and the next longer and next shorter road in
the route map differs significantly in the scaled and unscaled
route maps, a penalty is added to the variable "Score." The purpose
of function "RatioScore( )" is to preserve road length ratios in
the scaled route map from the unscaled route map that have
sufficient space.
In one representative target function used by an embodiment of road
layout module 686, "RatioScore( )" is represented by the following
expression:
For each road (A) whose length is greater than its minimum desired
length:
Compare the ratio of this road's length to the next shorter and
next longer road, capping the ratios at five, since in a
non-uniform cap it is hard to maintain any larger ratio. Assign a
penalty as: penalty=absolute(current ratio-original
ratio)*RATIO_SCORE
EndPointDirectionScore( ). The fifth function to contribute to the
variable "Score" in the representative code is function
"EndPointDirectionScore( )" (line 507). This function adds a factor
to the variable "Score" to reflect the difference in the
orientation between the start and end addresses in the unscaled
route map and in the scaled route map. The magnitude of the factor
added to the variable "Score" by this function is dependent upon
the extent of the difference in the orientation between the start
and end addresses in the scaled and unscaled route maps. Large
differences in the orientation yield a large magnitude while small
differences yield a small magnitude.
In one embodiment of road layout module 686,
"EndPointDirectionScore( )" is represented by the following
expression: penalty=absolute(original orientation angle-current
orientation angle)*ORIENTATION_SCORE
EndPointDistancescore( ). The sixth function to contribute to the
variable "Score" in the representative code is function
"EndPointDistanceScore( )" on line 508 of the representative code.
This function adds a factor to the variable "Score" that reflects
the difference in distance between the start and end point
addresses in the original unscaled route map and the current scaled
route map. This function is particularly useful for route maps that
have an overall U-shape. This function ensures that the start and
finish of the route map will not get too close to one another.
In one embodiment of road layout module 686,
"EndPointDistanceScore( )" is represented by the following
expression: penalty=(desired length=current length)/desired
length*DISTANCE_LENGTH
It will be appreciated that the scoring function represented by
lines 501 through 508 of the representative code merely illustrates
one type of scoring function that is used in some embodiments of
road layout module 686. In fact, many permutations of the scoring
function represented by lines 501 through 508 of the representative
code are possible. Such permutations include the use of only a
subset of the functions outlined in the representative code to
build the value of variable "Score." For instance, in some
embodiments, only the functions "IntersectionScore( )" and
"RoadLengthScore( )" are used. Other permutations of the scoring
function illustrated by the representative code include the
relative weighting of component functions so that some of the
functions have a greater influence on the value of the variable
"Score." Thus, for example, in some embodiments, the contribution
of IntersectionScore( ) to the variable "Score" is up weighted
relative to the contribution of "RoadLengthScore( )." Such
weighting schemes may be dynamically imposed based on factors such
as the complexity of the route, the size of the viewport used to
display the route, the presence of anomalies such as a road in the
route that is much longer than any other road in the route, as well
as user specified preferences.
Additional Label Refinement Embodiments
Another important aspect of the overall process for producing a
high quality map is performed by label layout module 688. Label
layout module 688 places and optimizes labels that correspond to
the various roads in the route map. One novel feature of label
layout module 688 is that it will fix the position of the label for
certain roads during refinement.
FIG. 9 illustrates one embodiment of label layout module 688 (FIG.
6). Many different types of target functions may be used to refine
the label position in the process illustrated in FIG. 9. Two such
target functions are described by lines 301 through 308 and lines
401 through 417 of the illustrative code. In the previously
described embodiments, a simulated annealing schedule was used to
place labels within a continuous range of positions in a region
around the center of the road corresponding to the label. Such a
region is called a constraint. The type of constraint used in
previously described embodiments is illustrated in FIG. 17A. In
FIG. 17A, element 1802 illustrates the continuous range of
positions that may be used to place the label that corresponds to
road 1802. Element 1804 serves as a constraint because the center
of the label is constrained to lie somewhere within element 1804.
FIG. 17B illustrates the placement of label 1806 at one such
acceptable location.
The layout module 688 described in this section builds upon the
constraint definition used in prior embodiments. The expanded
constraint definition is used by the target function in the
simulated annealing schedule of label layout module 688 to identify
a suitable label position, orientation, and style. The constraint
components in the expanded constraint definition include (i) a
bounding box (e.g. element 1704 in FIG. 17A), (ii) an orientation
(e.g. element 1710 in FIG. 17C), (iii) a layout style (e.g. FIG.
18A through 18F), and (iv) a scoring strategy.
The bounding box defines where the center of the label layout can
be positioned. Thus, in FIG. 17B, a label placed using the
constraint defined by box 1704 can be placed in such a manner that
the center of the label falls anywhere in box 1704. Orientation
vectors define how a label should be rotated. Label 1706 in FIG.
17A is positioned along a vector that is parallel to the long axis
of corresponding bounding box 1804. Using the expanded constraint
definition, labels can adopt alternative orientations. For example,
the label may be oriented so that it is orthogonal to the long axis
of the corresponding bounding box. FIG. 17D illustrates the
placement of a label in a rotated position.
The layout style defines what text and images are created and how
they are combined to make up the label when the given constraint is
selected during annealing. FIG. 18 provides a number of exemplary
layout styles. The layout style illustrated by FIG. 18A is a simple
layout style in which the primary name for a street or highway is
depicted. The layout style illustrated by FIG. 18B combines an
arrow image with the primary name for a street or highway. The
layout style illustrated by FIG. 18C combines the primary name for
a street or highway with the mileage along the road. The layout
style illustrated by FIG. 18D provides a highway number as text
stacked on top of a shield image. The layout style illustrated by
FIG. 18E provides word wrapping. Finally, the layout style
illustrated by FIG. 18F provides a highway number stacked on top of
a shield image with the mileage along the corresponding road.
The scoring strategy defines what base penalties are used with each
constraint. The magnitude of the base penalty for a particular
constraint is chosen by considering the type of layout style that
is associated with a constraint. For example, a layout style that
doesn't include a distance label (FIGS. 18A, 18E) is penalized more
than one that does (FIG. 18C). A representative scoring strategy,
in accordance with one embodiment of the present invention, is
provided in Table 1. Each layout style has a base weight and a
position score. In the scoring strategy provided by Table 1, lower
scores represent improved label positions. Furthermore, the scoring
strategy provided in Table 1 is designed to provide a target
function that allows layout module 688 to find optimal positions
for labels in the route map.
TABLE-US-00007 TABLE 1 Representative Scoring Strategy for Label
Positions Base Layout Style Weight Position Score Caveats Highway
Shield 0.0 +penalty * Applicable only to (distance from highways
with center of label to known highway center of numbers
corresponding road) Road name directly 0.1 +0.1 for below the above
or below road road versus above the road; + penalty * (distance
from center of label to center of road) Road name on road 0.3
+penalty * Applicable only to extension (distance from roads where
road center of label to continues past center of road) intersection
with next or previous road. (i.e. not a T intersection) Road name +
1.0 +penalty * aarrow pointing to (distance from tip of road arrow
to center of road); +penalty for angle between label, road and
screen; horizontal or vertical: +0.0; 90 degrees: +0.6; other:
+1.0
In the scoring strategy outlined in Table 1, the base score
assigned to a base layout style is further defined by (i) the
presence or absence of word-wrapping and (ii) whether there is no
distance label, a distance label directly to the right, or a
distance label directly below the label. Furthermore all position
scores in Table 1 are further determined by whether there is
distance labeling and word-wrapping. When there is no distance
label, an additional 1.5 units is added to the score and when the
road name is twenty characters or longer and there is no word
wrapping, an additional 1.0 units is added to the score.
Turning attention to FIG. 19, an illustrative preprocessing phase
in accordance with the present invention is illustrated. First, a
road 1902 in the route map is selected (FIG. 19A). Then, a random
constraint definition is chosen for the road from a set of possible
constraint definitions. Each constraint in the set of possible
constraint definitions includes a bounding box definition, an
orientation vector, a layout style, and a scoring strategy. For
example, constraint definition 1904 (FIG. 19B) includes the
illustrated bounding box, an orthogonal orientation, a primary name
plus distance layout, and a default scoring strategy. Other
possible constraint definitions besides arrow constraint 1904 are
possible. For example, in FIG. 19B, other possible constraint
definitions include extended road constraints and highway shield
constraints. The remaining steps in the illustrative preprocessing
stage are discussed with the assumption that constraint definition
1904 is selected by the preprocessing method. Once a constraint
definition has been selected, the next step is to randomly pick a
position within the bounding box that is associated with the
constraint. In FIG. 19C, such a position is illustrated by element
1910. Finally, using the layout style and orientation vectors
associated with constraint 1904, label 1912 for road 1902 is
positioned (FIG. 19D).
Turning attention to FIG. 20, an overview of the embodiment of
layout module 688 that makes use of expanded constraint definitions
is illustrated. The process begins with processing step 2002. In
processing step 2002 a set of potential constraint definitions is
associated with each label to be placed in the scaled route map.
Execution of processing step 2002 results in a set of potential
constraint definitions, such as those represented in FIG. 19B,
being associated with each label to be refined by label layout
module 688. It will be appreciated that processing step 2002 will
exclude constraint definitions that are not appropriate for a
particular label class. For example, a constraint definition that
includes a highway shield layout style will not be included within
the set of potential constraint definitions associated with a label
for a small road in the route map during processing step 2002.
During processing step 2004, a constraint definition is selected
for each label in the scaled route map from the set of constraint
definitions associated with each label during processing step 2002.
In one embodiment of layout module 688, an optimal constraint
definition is selected for each label from a set of heuristics.
Such heuristics include, for example, rules for specifying an
optimal constraint definition for a highway. In another embodiment
of layout module 688, no set of heuristics are used to choose a
constraint definition from the set of potential constraint
definitions and a constraint definition is randomly selected for
each label from the set of constraint definitions associated with
the label during processing step 2002. Once a constraint definition
has been chosen for a label in processing step 2004, the center of
the label is positioned within the bounding box associated with the
constraint definition in accordance with the orientation vectors
associated with the constraint definition. In one embodiment, the
center of the label is positioned at the center of the bounding
box. In another embodiment, the center of the label is positioned
at a random location within the bounding box.
In processing step 2006, a check is performed to determine whether
any label positions can be fixed. In the check, the boundaries of a
label are compared to the constraint boundaries of every other
label in the map. If there is no overlap between the boundaries of
a given label and the constraint boundaries of all other labels in
the route map, then the given label is fixed at its current
position since there is no possibility that the given label will
intersect another label during subsequent refinement. In some
embodiments, labels are only fixed in step 2006 if the constraint
definition selected for the label during processing step 2004 was
made based upon a set of heuristics designed to select an optimal
label. Thus, in such embodiments, when the constraint definition
selected during processing step 2004 is randomly selected, the
label is not fixed during processing step 2006.
During processing step 2008, an initial effective temperature t is
selected and counter i is set to one (2008). In processing step
2010, a label j from the set of labels that has not been fixed in
processing step 2006 is randomly selected. The quality of the
position of the j.sup.th label (S.sub.1) is measured using a target
function in processing steps 2012 and in processing step 2014 the
j.sup.th label is repositioned by positioning the label in
accordance with the bounding box, orientation vectors, and layout
style of a different constraint definition in the set of constraint
definitions associated with the j.sup.th label during processing
step 2002. In particular, the center of the j.sup.th label is
randomly positioned within the boundaries of the bounding box of
the different constraint definition. In processing step 2016, the
quality of the newly positioned j.sup.th label (S.sub.2) is
measured. The target function used during processing step 2012 and
2016 is any function capable of assessing the quality of a label
position in a route map. To this end, the target function could be
that of lines 301 through 308 or lines 401 through 417 of the
illustrative code described in other embodiments of label layout
module 688 above.
When the quality of the j.sup.th position has improved
(S.sub.2<S.sub.1) (2018--Yes), the new label position for the
j.sup.th label is accepted (2026). When the quality of the map has
not improved (S.sub.2>S.sub.1) (2018--No) there is a probability
1-exp.sup.-[(.DELTA.S)/k*t)] that the new label position for the
j.sup.th label will be accepted. The probability that the change in
label position will be accepted diminishes as effective temperature
t is reduced. The probability function is implemented as processing
steps 2020 through 2028 in FIG. 20. In processing step 2020,
exp.sup.-[(.DELTA.S)/k*t)] is computed. In processing step 2022, a
number P.sub.ran, in the interval 0 to 1, is generated. If
P.sub.ran is less than exp.sup.-[(.DELTA.S)/k*t)] (2024--Yes), the
change made to the j.sup.th label position in processing step 2014
is accepted (2026). If P.sub.ran is more than
exp.sup.-[(.DELTA.S)/k*t)] (2024--No), the change made to the
j.sup.th label position in processing step 2014 is rejected (2028).
It will be appreciated that probability functions other than the
function shown in processing step 2020 are within the scope of the
present invention. Indeed, any probability function that is
dependent upon effective temperature t is suitable.
Processing steps 2008 through 2028 represent one iteration in the
annealing process. In processing step 2030, iteration count i is
advanced. When iteration count i does not exceed the maximum
iteration count (2032--No), the process continues at step 2010.
When the iteration count equals a maximum iteration flag
(2032--Yes), effective temperature t is reduced and the stage
counter is advanced (2034). One of skill in the art will appreciate
that there are many possible different types of schedules that are
used to reduce effective temperature t in various implementations
of processing step 2034. All such schedules are within the scope of
the present invention. After processing step 2034, a check is
performed to determine whether the simulated annealing schedule
should be terminated (2036). When it is determined that the
annealing schedule should not end (2036--No), the process continues
at step 2008 with the re-initialization of iteration count i.
Layout Templates
Because route maps are often used when driving or navigating, it is
important to present the maps and text in a convenient format such
as a single 8.5 by 11 inch form. In one embodiment of the present
invention, each form contains several image templates, such as the
scaled route map or a conventional overview map, as well as text
boxes for text directions, estimated distance and time. In one
embodiment of the present invention, predefined forms are provided
that define the layout and size of each of the image templates and
text boxes. Exemplary image templates and text boxes are provided
in FIG. 21. FIG. 21A is a text box that provides header information
while FIG. 21B is an image template that provides a scaled route
map. There are different image template sizes to accommodate scaled
route maps of various sizes. FIG. 21C is a text box that provides
text directions, FIG. 21D is an image template that provides an
overview map, and FIG. 21E is an image template that provides a
detailed map.
Several factors are used to consider which image template to use
for a scaled route map. Such factors include, for example, the
estimated aspect ratio of the scaled route map (i.e. the ratio of
the total width of the scaled route map to the total height of the
scaled map), the number of elements (i.e. roads) in the scaled
route map, and the overall orientation of the scaled route map.
Exemplary code for one method for selecting an image template is
provided in lines 700 through 723 of the exemplary code.
TABLE-US-00008 (700) function SelectTemplate( ) { (701) aspectRatio
= map->EstimateAspectRatio( ); (702) int num_roads =
map->GetOrigNumSteps( ); (703) (704) if((aspectRatio < 0.60)
.vertline..vertline. ((aspectRatio < 0.70) && (num_roads
<= 15))) { (705) select skinny vertical image template for the
scaled route map (FIG. 22A) (706) if (num_roads < 20)
scaled_route_map_height = 500; (707) else { (708) // this is a long
route, so extra pixels in the vertical dimension // are required
(709) scaled_route_map_height = 700; } (710) else if (aspectRatio
> 2.0) { (711) select skinny horizontal image template for the
scaled route map (FIG. 22B) (712) else { (713) select square image
template for the scaled route map (FIG. 22C) (714) if (num_roads
< 15) scaled_route_map_height = 400; (715) else if (num_roads
< 25) { (716) // this is a long route (717)
scaled_route_map_height = 500;} (718) else { (719) // This is a
really long route (720) scaled_route_map_height = 600;} (721) } }
(722) adjust dimensions of text, overview map, detail map and
scaled (723) route map to defaults for this template}
In the exemplary code, the aspect ratio of the scaled route map is
estimated in line 701 and the number of elements or roads in the
route map is determined in line 702. In lines 704 and 705 of the
exemplary code, a decision to chose a skinny vertical image
template 2202 (FIG. 22A) for the scaled route map is made when the
estimated aspect ratio of the scaled route map is less than 0.6 or
when the aspect ratio is less than 0.7 and the number of elements
or roads in the scaled route map is less than 15. Skinny vertical
image 2202 has a variable height which is determined by lines 706
through 709 of the exemplary code. Accordingly, when the number of
roads in the route map is twenty or less, skinny vertical image
2202 is assigned a height of 500 pixels. When, the number of road
in the route map is more than twenty, skinny vertical image 2202 is
assigned a height of 700 pixels.
When the aspect ratio of the scaled route map is greater than 2.0
(line 710 of the exemplary code), skinny horizontal image template
2204 (FIG. 22B) is selected (line 711). For scaled route maps with
any other aspect ratio, square image template 2206 (FIG. 22C) is
selected (lines 612 613). Like element 2202, element 2206 is of a
variable height that is determined by the number of roads in the
scaled route map as set forth in lines 715 through 720 of the
exemplary code. Finally, in lines 722 through 723 of the exemplary
code, the dimensions of the remaining image templates and text
boxes 2250 that are provided in the output form are positioned
around the image template that includes the scaled route map to
yield a fixed dimension form 2260, 2270, or 2280.
Context Information
All the information depicted in a route map can be divided into two
categories: (1) route information and (2) context information.
Route information includes information that is necessary to follow
a route. Roads along the route and their labels are examples of
necessary route information. Context information is secondary
information that is not directly on the route, and is not needed
for communicating the basic structure of the route. Examples of
context information include landmarks, roads that intersect the
route (i.e. cross streets) and the names of cities, parks, or
bodies of water near the route. Context information can make it
easier to understand the geography of the route, provide validation
that the navigator is still on the correct route, and aid in
identifying important decision points along the route.
In one embodiment of the present invention, two basic types of
context information are handled: cross streets and point features.
In this embodiment, city names are considered as point features.
Adding context information to a route map requires first deciding
which context information should appear in the route map. This
choice is made difficult by the fact that context that is important
to one person is not necessarily important to another person.
Although some basic rules and preferences that can be used for
choosing context information are described in the following
example, it will be appreciated that the present invention is
fashioned so that any context selection algorithm can be used.
In one example, every major cross street intersecting the roads on
the main route of the route map, as well as the first cross street
after each turning point on the main route is added to a route map
as context information. The cross streets before the turn help the
navigator monitor progress up to the turn, and the last cross
street before the turn provides warning that the turn is coming up.
The first cross street after the turn helps the navigator determine
the proper turn has been missed. Three main classes of point
features useful for using a route map are: (i) highway exit signs,
(ii) buildings and businesses along the route and at turning
points, and (iii) city names. Preferably all highway exit signs,
particularly the exit number, are included because they make it
much easier for the navigator to figure out which exit to take to
get onto the next road on the route. Picking which business to
include is more difficult, as there is no simple way of identifying
the most salient building or businesses along a route. However, if
the map is designed for a particular business partner such as
McDonalds, all McDonalds along the route can be added
automatically. Finally, it is desirable to include all major city
names near the main route. For example, for a route between Santa
Cruz Calif., and Hayward Calif., labels for Cupertino, San Jose,
Milpitas, and Fremont are added to the route map as context
information. The cities are chosen based on their proximity to the
route, their population, and their area. City names help the
navigator understand the overall geographic position and
orientation of the route.
Once context information has been selected, it must be placed onto
the route map. Context can be placed by annotation module 690 any
time after the roads on the main route have been laid out by road
layout module 686 (FIG. 1). Context layout is generally performed
right after execution of label layout module 688. If context is
placed before label layout, the label layout scoring algorithm used
by label layout module 688 is modified to check for label-context
intersections. In one embodiment, selection of context information
to be depicted on the map is no guarantee that it will actually be
placed and rendered. If the context layout algorithm used by
annotation module 690 cannot find a good placement for the context
information, the algorithm can choose not to include this context
information.
In one embodiment of the present invention, the approach used by
annotation module 690 to place cross streets is very similar to the
approach used for placing point features in the route map. The
algorithm for placing cross streets will be described in detail
first. Then, the differences in the algorithm used in one
embodiment of annotation module 690 for placing point features will
be briefly described.
Placing cross streets. FIG. 23 shows a scaled route map with
several cross streets placed along the route. A cross street is
specified by (i) the point of intersection of the street with the
main route, (ii) the name of the cross street, (iii) shape points
defining the shape of the street and optionally, and (iv) the
importance of the cross street. The importance value for each cross
street can either be supplied or it can be computed as the first
step in placing the cross streets. In one embodiment, the names of
cross streets and their relative importance are obtained from
context database 696 (FIG. 1). In another embodiment, a predefined
rules are used for computing the relative importance of a
particular cross street. The last major cross street before a
turning point on the main route is considered relatively important
because such cross streets are helpful as a warning sign that the
turn is approaching. Thus these cross streets are given the highest
relative importance. In this embodiment, the cross road immediately
after the turning point is given the next highest importance
because such streets help navigators check if they missed the
proper turn. Cross streets are especially helpful near the route
destination, where presumably the navigator is less familiar with
the territory. Therefore these cross streets are given higher
importance than cross streets near the beginning of the route.
In the present invention, two search-based approaches to laying out
cross streets are provided. The first approach considers each cross
street, one at a time, in order of importance. If importance is
equal, a cross street is randomly picked from the equally important
cross streets. Then, a search for a "good" placement for the road
is performed. If a good placement is found, the cross road is drawn
in the rendering phase of the process. If a good placement is not
found, the cross street is not drawn during the rendering phase and
therefore is not included in the map.
The second approach to laying out cross streets searches for a good
placement of all cross streets simultaneously. All of the cross
streets are placed on the map. Each cross road may also be "hidden"
instead of being placed. Then the placements are optimized.
The first approach to laying out cross streets is faster than the
second approach but may not find an optimal placement for all of
the cross streets. The second approach to laying out cross streets
may take longer than the first approach but is less constrained and
may therefore produce a better overall placement.
Regardless of whether the first or second approach is taken by
annotation module 690 to lay out cross streets, a search-based
approach to optimizing the placement of the cross streets is
performed. This requires two basic functions: perturbation and
scoring. The perturbation function is used to change the layout of
a particular cross street while the scoring function evaluates the
current placement of the cross streets. The scoring function is
used in the search-based approach to determine whether the
perturbation improved the map layout. Such a determination is made
in accordance with a search algorithm. Representative search
algorithms that may be used include greedy algorithms, gradient
descent, simulated annealing, Tabu searches, and A* as reviewed by
Zbigniew et al. in How to Solve It: Modern Heuristics,
Springer-Verlag, Berlin, Germany, 2000, greedy searches A*/IDA*,
simulated annealing and hill climbing (gradient descent) as
reviewed by Russell et al. in Artificial Intelligence: A modern
Approach, Prentice Hall, 1995, and genetic algorithms as reviewed
by Goldberg in Genetic Algorithms in Search, Optimization and
Machine Learning, Addison-Wesley, 1989.
In one embodiment, the perturbation function is designed as
follows:
Perturb( ) randomly pick one of the following variables and change
it: the position of a cross street's intersection with the main
path; the position of cross street label; or whether the cross
street is included in the map or is "hidden"
When Perturb( ) changes the position of the cross street label, the
perturbation is subject to the constraint that the street label
falls within a predetermined area that includes the cross street's
intersection. In one embodiment of the present invention, the shape
of the predetermined area is a square and the square is centered on
the cross street's intersection. Accordingly, the position of the
cross street label that is associated with the cross street can be
perturbed by an amount as long as the cross street label remains in
the square. Once the position of the cross street's intersection
with the main path and the cross street's label are chosen, the
cross street is extended to pass under or over its label and to
pass slightly beyond the intersection with the main route.
In one embodiment, the scoring function that is used to evaluate
perturbations is designed as follows:
Score( ) the placement of each cross street is scored based on
several criteria as follows: a distance between the current
intersection point of the cross street and the main path and the
true intersection point between the cross street and the main path;
a number of other objects in the map that overlap the cross street,
weighted by the amount of overlap; a number of other objects in the
route map that overlap the cross street's label, weighted by the
amount of overlap; a position of a cross street label along a cross
street, using the same constraint-based scoring as in normal label
layout; an amount of visual clutter/density around the cross
street; and whether the cross street is hidden; hiding a cross
street is penalized by an amount proportional to its importance,
thus encouraging the search to place the cross streets rather than
simply hide all of them. The most complicated aspect of the scoring
criteria is the notion of visual density or clutter. The present
invention encompasses several different methods for computing
visual density for a fixed region of focus centered at the cross
street/label. To appreciate these methods, reference is made to
FIG. 24 which shows a portion of a route map 2402 that includes an
area of focus 2404 with a cross street for which a measure of
visual clutter is sought. Using FIG. 24 as a reference,
representative metrics include:
(1) Convolve a pixel based image of the route map with a Guassian
kernel in focus region 2404 using the luminance value of each pixel
within the focus region.
(2) Compute the area of each object in focus region 2404 multiplied
by the average luminance for the object. Box 2406 drawn in FIG. 24
illustrates the area of one object in focus region 2404. The
product of the multiplication of object area and average luminance
is divided by distance from center of cross street to the center of
object. Visual density is set to sum over all objects in the focus
region. An equation that describes this metric is:
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times..times..times..times..times..times..tim-
es..times..times..times..times..times..times. ##EQU00001##
Metric (1) is computationally expensive. Metric (2) is a quicker,
but less accurate approximation of visual density. When laying out
one cross street at a time, alternations are made between
perturbing and scoring until the score reaches some acceptable
threshold, and the placement is kept, or the iteration count
reaches some maximum. If the score never goes below the threshold,
the cross street is not included in the route map. When laying out
all cross streets at once, a variety of search-based algorithms to
minimize the overall score may be used. In such embodiments,
overall score is computed as the sum of the scores for each cross
street. Representative search-based algorithms that may be used
include greedy algorithms, gradient descent, simulated annealing,
Tabu searches, and A* as reviewed by Zbigniew et al. in How to
Solve It: Modern Heuristics, Springer-Verlag, Berlin, Germany,
2000, greedy searches A*/IDA*, simulated annealing and hill
climbing (gradient descent) as reviewed by Russell et al. in
Artificial Intelligence: A modern Approach, Prentice Hall, 1995,
and genetic algorithms as reviewed by Goldberg in Genetic
Algorithms in Search, Optimization and Machine Learning,
Addison-Wesley, 1989.
Placing point features. FIG. 25 shows a route map with several
point features, such as exit numbers, restaurant locations and city
names included. A point feature is specified by:
An ideal (latitude, longitude) location for the point feature and
either a circular or linear constraint region specifying the
acceptable positions for the point feature. In the case of a city
name, the feature would be allowed to appear any where within a
circle inscribed in the boundary of the city. This region must be
warped into the non-uniform coordinate system of the map;
the feature name, or an image, to be shown at the feature location;
and
optionally, the importance of the feature.
Just as in the case of cross streets, the importance of a point
feature may be provided or may be computed during the layout. In
one embodiment, all highway exit signs are given equal importance
unless their importance values are provided a priori. For city
names, importance is computed by multiplying the proximity of the
city region to the route, the population of the city and the area
of the city. Thus in this embodiment, large cities, with high
populations, near the route are considered most important.
Buildings and businesses are given higher importance when they are
at intersections as opposed to along the roads in the route map.
Furthermore, according to this embodiment, higher importance is
allocated to businesses that are on smaller roads near the
beginning or end of the route than those that are on larger roads
such as highways and freeways.
As with cross streets, point features can be placed one at a time,
or all at once. The ideal location and its surrounding constraint
region is well-defined in the original coordinate system of the
constant scaled map. To place point features we must first warp the
ideal point and constraint region into the non-uniform coordinate
system of the scaled route map. Because the coordinate system is
non-uniform, a constraint-based optimization procedure is used to
perform the warp. A variety of constraint-based warping techniques
have been developed and are known as morphing techniques. See, for
example, Beier and Neely, "Feature-Based Image Metamorphosis,"
Proc. SIGGRAPH '92, 3 42 (1992). Furthermore, for a general
overview of warping techniques see Gomes et al., "Warping and
Morphing of Graphical Objects," Morgan Kaufmann (1998). Any of the
methods described in these references can be used to warp the ideal
point and constraint region into the non-uniform coordinate system
of the scaled route map.
The main differences in the search-based layout between cross
streets and point features are in the perturb and score functions,
which we describe below. When refining point features the perturb
and score function has the format:
Perturb( ) Randomly pick one of the following variables and change
it the position of the point feature within the region of
acceptable positions. whether the point feature is included in the
map.
Score( ) The placement of each point feature is scored on the
criteria: the number of other objects in map that overlap point
feature, weighted by the amount of overlap; the distance between
current location of point feature and its ideal location; whether
the point feature is hidden-again the penalty is proportional to
the importance of the point feature; and amount of visual
clutter/density.
Verticalization Techniques
In some embodiments of the present invention, memory 668 of server
computer 624 includes a map verticalization module 698 (FIG. 6).
Map verticalization module 698 is used to optimize the orientation
of the scaled route map with respect to the dimensions of a given
viewport. Map orientation optimization is particularly advantageous
in instances where the viewport size used to display the scaled
route map is small. In such situations, only a portion of the
scaled route map is typically displayed. When just a portion of the
scaled route map is displayed, the user is provided with the option
to scroll the scaled route map in order to view the full route. To
avoid confusion, it is advantageous to orient the scaled route map
such that the long axis of the scaled route map coincides with the
scroll direction. In one embodiment, the scroll direction is
vertical and the scaled route map is oriented by map
verticalization module such that the long axis of the scaled route
map is vertical. Alignment of the long axis of a scaled route map
with the scroll direction maximizes the amount of information that
is displayed in a miniature viewport and provides a convenient
mechanism for delivering consistent map layouts. The user can
review the full rotated scaled map by using the scroll option.
Map verticalization is particularly advantageous in hand held
devices such as personal digital assistants ("PDAs"). Given the
dimensions of the viewport of a typical PDA, it is desirable to
offer scaled route maps having the dimensions constant by Y, where
Y varies in accordance with the number of steps or distance of the
route within the route map. Thus, if the route is fairly short, the
entire scaled route map is displayed in the PDA viewport. However,
if the route includes several steps and has a fairly extensive long
axis, the long axis is oriented so that it is aligned with a scroll
bar. In this way, the consumer gets a consistent layout with only
vertical scrolling.
Now that an overview of the advantages of map orientation have been
discussed, a method for computing the orientation of the map is
described. First, the position of each intersection along the main
path in the scaled route map is computed. These intersection points
are then fitted with a probability distribution. The probability
distribution could be, for example, a binomial distribution, a
Poisson distribution, a Gaussian distribution, or any other
suitable probability distribution. When a Gaussian distribution is
used, the center of the distribution is the mean of the
intersection points, the axes of the distribution are the
eigenvectors of the covariance matrix., and the extents of the
distribution are the eigenvalues of the covariance matrix. The
probability distribution defines axes and extents along those axes
for the route. As illustrated in FIG. 11A, from these axes, the
tightest bounding box 1100 that contains the complete route is
determined. From bounding box 1100, the longest (dominant) axis of
the route is computed. The direction of the longest axis is used to
determine the amount by which the scaled route map is rotated so
that it runs in a predetermined direction. In FIG. 11, the start of
the route is marked by a hashed circle and the end of the route is
marked by an open circle. Since the start point of the route is
known, it is possible to perform the rotation of the map so that
the start location is always at the bottom (FIG. 11B) or always at
the top (FIG. 11C) of the viewport. Thus, the verticalization
method is used to ensure that limited viewport space is fully
utilized and to ensure that the starting location of each displayed
map consistently lies in the same region of the viewport.
It will be appreciated that if the aspect ratio of the probability
distribution used to determine the axes of the scaled route map
indicates that the map is roughly square, verticalization is not
performed. In one embodiment, the probability distribution used is
a Gaussian distribution and verticalization is not preformed when
the aspect ratio of the scaled route map is less than or equal to
1.98.
Sample code used to compute the long axis in a scaled route map and
to rotate the scaled route map is provided below.
TABLE-US-00009 (801) bool Map::Verticalize( ) (802) { (803) Vector2
mapOrientation[2]; (804) double extents[2]; (805)
GaussPointsFit(numIntersectionPts, intersectionPts, center, axes,
extents); (806) // Verticalize map only if aspect ratio in obb
coordinates is > // 1.98 (807) // Compute the aspectRatio as
extent[1]/extent[0] as it should be (808) // since the second
extent is sorted to be the longest axis. (809) double aspectRatio =
extents[1]/extents[0]; (810) if (aspectRatio >= 1.98) { (811) //
Assume the mapOrientation vectors are of unit length. The (812) //
orientation vectors are sorted in increasing order, so use the
(813) // second one to compute the rotation angle. (814) double
angle = atan2(mapOrientation[1].v,mapOrientati- on[1].u); (815)
Rotate(-angle); (816) return true; (817) } (818) return false;
(819) } (820) void GaussPointsFit (int NumPoints, const Vector2*
Point, (821) Vector2& Center, Vector2 Axis[2], double
Extent[2]) (822) { (823) // Compute mean of points. (824) for (int
i = 1; i < NumPoints; i++) (825) Center += Point[i]; (826)
Center /= NumPoints; (827) // Compute covariances of points (828)
double SumXX = 0.0, SumXY = 0.0, SumYY = 0.0; (829) for (i = 0; i
< NumPoints; i++) (830) { (831) Vector2 Diff = Point[i] -
Center; (832) SumXX += Diff.u*Diff.u; (833) SumXY += Diff.u*Diff.v;
(834) SumYY += Diff.v*Diff.v; (835) } (836) SumXX /= NumPoints;
(837) SumXY /= NumPoints; (838) SumYY /= NumPoints; (839) // solve
eigensystem of covariance matrix (840) Eigen E(2); (841) E(0,0) =
fSumXX; (842) E(0,1) = fSumXY; (843) E(1,0) = fSumXY; (844) E(1,1)
= fSumYY; (845) E.SolveEigenSystem( ); (846) Axis[0].u =
E.GetEigenvector(0,0); (847) Axis[0].v = E.GetEigenvector(1,0);
(848) Axis[1].u = E.GetEigenvector(0,1); (849) Axis[1].v =
E.GetEigenvector(1,1); (850) Extent[0] = E.GetEigenvalue(0); (851)
Extent[1] = E.GetEigenvalue(1); (852) }
In line 805 of the sample code, a call to procedure GaussPointsFit
is made. Procedure GaussPointsFit is coded by lines 820 through 852
of the sample code. On lines 823 through 826 of the sample code,
procedure GaussPointsFit computes the mean of all the intersections
in the scaled route map. On lines 827 through 838 of the sample
code, procedure GaussPointsFit computes the covariances of the
intersections. On lines 839 through 851 of the sample code,
procedure GaussPointsFit solves the eigensystem of the covariance
matrix. This information is used in the main body of the sample
code. More specifically, in line 809 of the sample code, an aspect
ratio is computed. As defined herein, the aspect ratio is the ratio
of the lengths of the two axes corresponding to the scaled route
map, as determined by procedure GaussPointsFit. In the embodiment
described by the illustrative code, the scaled route map is not
reoriented if the aspect ratio is less than 1.98. If the aspect
ratio is equal to or greater than 1.98, than the scaled route map
is rotated so that the longest of the two axes computed by
procedure GaussPointsFit lies in a predetermined direction, such as
vertical. This rotation is performed by lines 814 and 815 of the
sample code.
Although the above example describes the verticalization of a
scaled route map, it will be appreciated that the verticalization
technique is not limited to scaled route maps. Indeed, any image
that has a collection of points that can be fitted by a probability
distribution can be optimized for display on a viewport using the
verticalization techniques.
Finding Empty Space
As discussed previously, annotation module 690 (FIG. 6) is used to
place landmarks and other annotations on the scaled route map in
order to help guide the user. However, identifying regions of the
map that are suitable for the placement of such annotations
presents a special problem. Simply stated, the problem is the need
to use efficient methods to identify suitable regions of the map to
the place the annotations. Suitable regions are regions of the map
that are not overpopulated with other objects. In FIG. 12, North
arrow annotation 1202 is added to the route map to indicate
direction. In one embodiment of the present invention, the
placement of North arrow annotation 1202 is constrained to the
upper left quadrant of the map in order to present a consistent
appearance between maps. Thus, the problem posed by FIG. 12 is the
identification of regions in the upper left hand corner of the
route map that are suitable for the placement of North arrow
annotation 1202.
FIG. 13 details the processing steps used to efficiently identify
free space in a route map in accordance with one embodiment of the
present invention. This free space is used to place annotations and
labels in the route map. In processing step 1302, the map is
partitioned into a grid. Typically, the grid used in processing
step 1302 is uniform, so that each grid cell is the same size. The
number of objects in the route map that touch each grid cell
produced in processing step 1302 is tracked. In this way, it is
possible to determine discrete areas of the route map that have
relatively few objects. In processing step 1304, candidate grid
cells into which the target annotation may be placed are
identified. In some embodiments, the region in which candidate grid
cells are searched for is restricted to a specific region of the
route map. In one example, each city label is assigned a bounding
region in which the label may be placed. This bounding region is
near the actual city in the route map.
When the annotation or label is larger than a single grid cell,
processing step 1306 is used to search for grid cells with
sufficient vacant adjacent grid cells to contain the object. If no
candidates are found after search 1306 (1308--No), a grid
subdivision scheme (1310) is initiated. Such a subdivision is
necessary in order to search through the map at a higher resolution
in order to identify a set of adjacent grid cells that can be used
for the annotation or label.
Processing step 1310 is implemented using any one of several
different possible grid subdivision schemes. For example, a number
of schemes that have been used to partition three-dimensional space
in disciplines such as ray tracing can be adopted for use in two
dimensional route map space. Such schemes are found in An
Introduction to Ray Tracing, Ed. Andrew S. Glassner, Academic
Press, Harcourt Brace Jovanovich, Publishers, New York (1989). In
one embodiment, the grid subdivision scheme used in processing step
1310 is a form of uniform spacial separation such as that discussed
in Section 5.2 of An Introduction to Ray Tracing id. For example,
in one uniform spacial separation grid scheme, each original grid
cell is divided into four cells. In another embodiment, the grid
subdivision scheme used in processing step 1312 is nonuniform
spacial subdivision such as that discussed in Section 5.1 of An
Introduction to Ray Tracing id. Nonuniform spacial subdivision
techniques are those that discretize space into regions of varying
size as a function of the density of objects present in the space.
Thus, in a nonuniform spacial subdivision approach, portions of the
route map that are more densely occupied by objects such as roads,
labels and annotations, are divided into smaller grid cells than
portions of the route map that are sparsely populated.
After the route map has been subjected to a grid subdivision scheme
in processing step 1310, the process continues by looping back to
processing step 1304. When processing step 1304 is reexecuted, a
search for candidate grid cells into which the label or annotation
can be placed is conducted using the grid subdivision generated in
processing step 1310. Furthermore, when the annotation or label is
too big to fit into a single grid cell, a search for adjacent grid
cells that can collectively accommodate the label or annotation are
identified. Processing steps 1304, 1306, 1308 and 1310 are repeated
until a candidate position is found in the route map (1308--Yes).
In some embodiments, processing steps 1304, 1306, 1308 and 1310 are
only repeated a predetermined number of times. If, after processing
steps 1304, 1306, 1308 and 1310 have been repeated a predetermined
number of times and a candidate position has still not been
identified, the annotation is rejected and not placed on the route
map. In some embodiments, when a label or annotation has been
geometrically constrained to a particular region of the route map
and no candidate position has been found in the route map, step
1304 and/or 1306 is repeated using less strict constraints. For
example, when a city label is restricted to be within a fixed
region of the geometric center of a city in the route map and no
candidate position is identified in the fixed region during a first
pass through processing steps 1304, 1306, 1308 and 1310, processing
step 1304 and/or 1306 is repeated using a larger fixed region
centered on the position of the city in the route map.
When processing step 1304 or 1306 identifies multiple candidate
positions in which to place the target label or annotation
(1312--Yes), the candidates are ranked by a ranking mechanism that
considers the density of objects in the grid cells that neighbor
the candidate position. In some embodiments, the candidate position
that has neighboring grid cells with the lowest occupancy is
selected. In other embodiments, other factors in addition to the
occupancy of neighboring cells in considered. For example, in some
embodiments, the candidate ranking is a function of both the
occupancy of neighboring cells as well as the absolute distance
between the candidate position and some reference point. In such
embodiments, candidate positions that are closer to a reference
point are up weighted relative to candidate positions that are
further away from a reference point. Such ranking embodiments are
useful for city labels, road labels, and for the placement of
geographical landmarks. When a single candidate position has been
selected by processing step 1314, or a single candidate position
has been found by processing step 1306 (1316), the annotation or
label is placed at the candidate position and the process ends
(1318).
FIG. 14 illustrates how the spacial subdivision of a route map is
used to identify grid cells suitable for the placement of North
arrow annotation 1202. In FIG. 14, the route map is partitioned
into a grid in accordance with processing step 1302 (FIG. 13). A
candidate grid cell into which an annotation may be placed is
identified in processing step 1304. In this example, step 1304 is
restricted to the top left corner in order to consistently place
the North arrow annotation 1202 in this region of the map. Because
step 1304 successfully identified a candidate grid cell using the
initial partition computed in processing step 1302, there is no
need to initiate a grid subdivision scheme 1310 and repeat
processing steps 1304, 1306 and 1308. Rather, North arrow
annotation 1202 is placed in an empty grid cell that is bordered by
grid cells having the lowest possible occupancy in accordance with
processing step 1314.
FIG. 15 illustrates a situation that arises when processing step
1304 and/or 1306 (FIG. 13) attempts to identify a grid cell or set
of contiguous grid cells in a constrained area and no candidate
grid cells are identified. In FIG. 15, label "Somewhere, USA" 1502
is constrained to the area identified by oval 1504. However, the
initial grid generated by processing step 1302 (FIG. 13) has failed
to produce a suitable candidate grid cell (1308--No). Therefore,
grid subdivision scheme 1310 is executed. FIG. 16 depicts the route
map after uniform spacial separation is used to subdivide only
those grid cells in the constrained area of the route map. In this
subdivision, each of the original grid cells in the constrained
area is subdivided into four new grid cells. Then, processing steps
1304 and 1306 are repeated using the new grid scheme. Because label
"Somewhere, USA" 1502 is too large to fit in the new grid cells,
processing step 1304 will fail. However, when processing step 1306
is executed, a candidate position that is composed of two adjacent
grid cells is identified and the label is placed at the identified
candidate position (1308--Yes, 1312--No, 1316, 1318). FIG. 16 shows
the placement of label "Somewhere, USA" 1502 after execution of
processing step 1318.
In some embodiments of the present invention, the spacial
subdivision scheme used in processing step 1310 is facilitated by
the use of a hierarchical data structure known as the region
quadtree. See e.g. Applications of Spacial Data Structures, Hanan
Samet, Addison-Wesley Publishing Company, New York (1990), pp. 2 8.
A region quadtree is a hierarchical data structure that is based on
the successive subdivision of a bounded image array into four
equal-sized quadrants. In the classical application of a region
quadtree, if a given array does not consist entirely of ones or
entirely of zeros, it is subdivided into quadrants, subquadrants,
and so on, until blocks are obtained that consist entirely of ones
or entirely of zeros. In this way, the image is subdivided using a
variable resolution data structure. The region quadtree is used in
some embodiments of the present invention in grid subdivision
scheme 1310. In such embodiments, the grid subdivision scheme only
subdivides selected grid cells in the initial grid. Typically, grid
cells that are selected for subdivision are chosen from the
constrained area.
Trip Tiks and Insets
In some instances, when scaling a map non-uniformly, it is
difficult to make all roads visible within a given viewport.
Because of this difficulty, some embodiments of the present
invention include a map division module 699 (FIG. 6). Map division
module 699 makes use of insets and/or triptiks when it is difficult
to make all roads visible within a given viewport. Map division
module 699 includes algorithms for determining when insets and
triptiks should be used within a scaled route map. When a
determination is made that an inset should be made, map division
module decides which portion of the map should be inset, and where
the inset should be placed within the main scaled route map.
Trip Tiks. When a route contains a large number of roads or
segments, it may not be possible to scale all the roads so that
they are large enough to be readable and yet within the image size.
In this situation it is desirable to break the scaled route map up
into several separate segment maps. In one embodiment of the
present invention, map division module 699 uses the following
algorithm to determine whether a scaled route map should be split
into a set of segment maps: generate an intermediate map that
includes each road (element); define a maximum number of elements
(M) allowable in any given map; and when a map contains S roads
(elements), where S>M, then divide the map uniformly into N
segment maps such that N>=S/M. However, in some instances
additional issues are considered. One such issue is the means by
which the main route in the route map is connected across a
plurality of segment maps. Various methods for depicting such
connectivity information in some embodiments of map division module
699 include: use of a special connection point icon at the endpoint
of the last road on a first segment map and use of the same special
connection icon at the start point of the first road on the
subsequent segment map; and sharing some roads between each pair of
successive segment maps. In addition, connectivity between
successive segment maps is insured by preserving the shape of the
main route and in particular the shape of any shared roads across
successive segment maps. To insure that the shape of shared roads
across successive segment maps remains exactly the same in each
segment map, shape simplification is preferably done for the entire
route in the intermediate map as a whole, as opposed to separately
in segment maps.
The problems map division module 699 is designed to alleviate and
the algorithms used in some embodiments of map division module 699
are illustrated with reference to FIGS. 26 through 28. FIG. 26
describes an entire route in a single image 2602. Although the
entire route is visible, the map is very cluttered and would be
difficult to use while driving. Furthermore, if the route had more
roads (elements) it would not be possible to label all of the roads
on the route. FIG. 27 splits image 2602 (FIG. 26) into two separate
segment maps 2702 and 2704 which, taken together, comprise the
route map of FIG. 26. The directions in segment maps 2702 and 2704
are more readable and comprehensible than the corresponding
directions in image 2602.
Turning to FIG. 28, the importance of preserving shape of shared
roads across successive segment maps is illustrated. In FIG. 28A,
an intermediate map 2802 that is about to be split into two segment
maps at breakpoint 2804 between element "CA-17" and "Cabrillo
Freeway" is shown. In FIG. 28B, intermediate map 2802 has been
split into segment maps 2810 and 2820. Both segment maps 2810 and
2820 have full shape. In contrast, in FIG. 28C intermediate map
2802 has been split into segment maps 2830 and 2840 that do not
retain the original shape of intermediate map 2802. That is, in
FIG. 28C, the route shape has been simplified separately in segment
maps 2830 and 2840. As a result, element 2834 "Cabrillo Fwy" has
different shape in segment maps 2830 and 2840. FIG. 28C represents
an undesirable representation of the overall route corresponding
elements in successive segment maps, i.e. "Cabrillo Fwy" have
different shape. A more desirable situation is represented in FIG.
28D. In FIG. 28D, route shape simplification is performed on the
intermediate map 2802 prior to splitting the intermediate map into
segment maps 2850 and 2860.
Some routes, termed multi-segment routes, contain multiple way
points between the start point and the end point of the main route.
Multi-segment routes are handled much like trip tiks in one
embodiment of the present invention. Accordingly, the multi-segment
route is split into separate segment maps at each way point: the
first image shows the route from the start point to the first way
point, the second image shows the route from the first way point to
the second way point, etc. With multi-segment routes, the same
convention of repeating a connection icon, in this case a way point
icon, and/or a set of shared roads is used across successive maps.
Moreover, simplification preferably occurs before splitting the
route so that the shape of each road and the overall shape of the
route do not change in each image.
Insets
In the map rendering phase two goals are optimized. The first goal
is to ensure that all roads in the route map are large enough to be
legible. The second goal is to maintain the overall shape of the
route, as well as the position of all intersection points between
roads. Despite the flexibility in scaling roads provided by the
present invention, it is difficult to attain both goals for some
routes in a single image. FIG. 29 illustrates how it is sometimes
difficult to fully optimize for both goals. In the scaled route map
2902 depicted in FIG. 29, it is readily apparent that:
1) Some roads remain very small in order to maintain the overall
shape, or to maintain intersection points. Legibility has been
sacrificed in favor of minimizing shape and topological
distortions.
2) The scaling of many small roads causes the overall shape of the
route to distort severely. In this case, overall shape has been
sacrificed in order to maintain legibility.
3) The scaling of short roads so they are legible causes a false
intersection. In this case, overall topology has been sacrificed to
maintain readability
One solution for such routes is to find the set of roads that must
remain small to maintain topology or intersection points and to
show them in a separate inset image. For example, in FIG. 29, to
maintain the intersection between I-74 (2904) and E. Cabin Town Rd
(2906) all the roads between the two roads are kept very short. By
including inset 2908, however, it is possible to enlarge the labels
of the roads between 2904 and 2906 and label these intermediate
roads as well. Additional examples of scenarios in which insets are
beneficial are provided with reference to FIGS. 30 and 31. In FIGS.
30 and 31, short roads that cause distortion or false intersections
are placed at an enlarged size in circular inset 3002 and 3102
respectively. By placing short roads in an enlarged inset, the
corresponding roads can be shorted in the main scaled route map to
the point where the overall shape distortion of the route is
acceptable or the false intersection is avoided. In one embodiment,
the inset image is created by running the entire map layout
algorithm coded by road layout module 686 on just the roads in the
inset. Roads that are shown in the inset and are too small to label
in the main scaled route map are labeled only in the inset.
Furthermore, in one embodiment, a unique boundary is placed around
the inset region in the main route map and the same unique boundary
is placed around the corresponding inset image to help the
navigator correlate insets to the main route map. Moreover, the
inset image is placed close to the feature of the main map it
depicts. In FIG. 30, the route shown in map 3004 is in fact almost
entirely North-South. However, the scaling of the small roads at
the end of the route has made the route appear to be almost
circular. This is an example of severe shape distortion that is
possible on such route maps after individual roads in the route
have been scaled. Using inset 3002, small roads are kept at their
original size in main map 3006, thus preserving a proper overall
North-South orientation. Simultaneously, the small roads are
enlarged in inset 3002 to make them legible in the insert. In FIG.
31, the scale of smaller roads such as "US-6", "W. 36th Ave", and
"Wilkes Ave" so that they are legible has introduced a false
intersection between "Wilkes Ave." and "US-61" in the route map. By
using inset 3102 the three roads can be grown to be large enough to
be visible without introducing the false intersection.
In one embodiment of the present invention, there are three steps
to creating an inset. First a determination is made as to which, if
any, roads to place in an inset, second the image size of the inset
is determined and finally, sufficient space to place the inset in
the main map image near the inset feature is identified. With this
overview of the process in this embodiment, the three steps will
now be described in more detail.
Selecting inset roads. The process begins by attempting to layout
all the roads in a single route map without insets. After the
initial layout a search is made for sets of roads that are very
short (in pixel size) as well as tight intersection loops. A check
is also made to determine if there is excessive shape distortion in
the overall shape of the route by checking how well the orientation
vector between the start and destination point of the overall route
is maintained. If it is not well maintained, a search for adjacent
sets of short roads, such as in a mile length of the main route,
that were grown excessively and are in the direction of the
distortion is made. Such sets of short roads are placed in an inset
and the main route map is re-scaled so that the excessively grown
roads are reduced to a more accurate scale. Finally a search for
false intersections is made. All roads in the loop created by the
false intersection are placed in the inset and the roads in the
loop are re-scaled in the main route maps to remove the false
intersection.
Inset image size. The size of the inset is chosen by first
estimating the aspect ratio for the set of roads that will appear
in the inset using the same procedure as described for choosing
layout templates. This gives an aspect ratio for the inset image.
Next a scale factor for the inset image is chosen. The scale factor
can be set a priori as a fixed number (i.e. 100 pixels) or can
dynamically be computed as a scale factor based on the number of
roads to appear in the inset (i.e. the scale factor equals thirty
times the number of roads in inset). Then, the pixel size of the
inset image is simply the scale factor multiplied by the aspect
ratio.
Placing an inset in a scaled route map. It is desirable to place
the inset in the main map image without overlapping any of the
objects in the main image. Thus, the inset should be placed close
to the feature of the main map it depicts so that the navigator
understands the relationship of the inset to the main map. A search
is made for empty space in the main map image using the techniques
described for finding empty space. The search begins in the main
image grid cell containing the features shown in the inset and
spirals around the image from this cell until free space large
enough to show the inset is found.
Road Shape
In another aspect of the present invention, novel algorithms for
simplifying the shape of a route are used. Most roads can be
immediately simplified to straight lines and this is in fact
perceptually preferable. However, some roads must maintain some
curvature and the orientation and layout of intersections between
two roads must be kept true to reality. In some embodiments of the
present invention, road shape simplification is not implemented.
Rather, each road in the route (or path) is specified as a single
linear segment. In embodiments in which road simplification is
applied, the route map is processed by road simplification module
697 prior to execution of road layout module 686. Rather than
treating each road as a single linear segment, road simplification
module 697 considers each road as a piecewise linear curve, i.e. by
a set of (lat,lon) shape points connected by linear segments. The
goal of road simplification module 697, then, is to reduce the
number of shape points in each road thereby simplifying the
roads.
There are two main reasons to simplify each road in a road map. The
first and most important reason is that roads with simpler shape
are perceptually easier to interpret as separate entities, and the
resulting route map has a cleaner, uncluttered look. See FIG. 32
for a comparison of the same route without (FIG. 32A) and with
(FIG. 32B) curve simplification. Second, simpler roads containing
fewer segments require less memory and are faster to process by
road layout module 686 in the subsequent layout stages. For
example, to compute the intersection of two roads requires looking
for an intersection between each pair of segments in each road.
With fewer segments per road this operation becomes much
faster.
Avoiding False/Missing Intersections. In one embodiment, before
simplifying roads, road simplification module 697 computes all the
intersection points between each pair of roads. Consider the
situation where roads r.sub.1 and r.sub.2 intersect at the points
P.sub.1, P.sub.2 and p.sub.3 in FIG. 34. Road simplification module
697 inserts each intersection point into the set of shape points
for both r.sub.1 and r.sub.2, and marks these intersection points
as retained, as shown in FIG. 34. More specifically, the original
sequence of shape points for r.sub.1 is (s.sub.1, s.sub.2, s.sub.3,
s.sub.4, S.sub.5, and s.sub.6). Three new intersection points are
inserted into this sequence, one for each intersection, resulting
in the sequence (s.sub.1, p.sub.2, s.sub.2, s.sub.4, p.sub.2,
s.sub.4, s.sub.5, s.sub.6, and p.sub.3). Similarly, these
intersection points are inserted into the sequence for r.sub.2 as
well. Since these intersection points can no longer be removed, the
simplification algorithm cannot cause any missing intersections.
Moreover, road simplification module 697 maintains a separate list
of all the true intersection points between roads. In subsequent
stages, simplification algorithm module 697 only accepts removal of
one or more shape points if the removal does not create a new
intersection point (i.e. an intersection point is not in the
original intersection points list). In this way module 697 ensures
that simplification does not generate any false intersections.
In some embodiments of the present invention, data cleanup is
performed after intersection points have been marked as retained.
Most roads depicted in a route map intersect with at least two
other roads: the previous road in the route at the road's start
point and the next road in the route at the road's end point. These
intersections are called "turning points" rather than
"intersections." At a turning point, the navigator switches from
following one road to following a different road. The term
"intersection" is used to refer to all other intersections between
roads. At intersections, the road being followed does not change.
It is extremely rare for two adjacent roads along the route to join
at both a turning point and also intersect with one another in a
separate location. If they did, the navigator would have turned
onto the second road at the earlier intersection rather than the
turning point (see FIG. 35). However, some highway on- and
off-ramps are exceptions to this rule. Consider some road A that
connects to a ramp which then passes under road A. From the two
dimensional overhead perspective of the route map, the ramp
intersects road A and then goes on to connect with the highway.
Module 697 forces such ramps to be like the other roads by moving
all the shape points between the turning point and the intersection
point in road A into the ramp. Then road layout module 686 assumes
that adjacent roads never intersect one another and thereby the
costly intersection computation between these roads is avoided.
Also, when the circular ramp is scaled by road layout module 686,
the entire circle is scaled as a unit thus avoiding concerns about
properly placing the intersection between the ramp and the previous
road.
Choosing Points to Remove/Retain from non-ramps. For roads that are
not ramps, a very aggressive protocol is used by road
simplification module 697 to smooth such roads. For a given road in
the route, the module initially marks every shape point except the
first, last, and any intersection points as removed. A pointer to
the second shape point and the second to last shape point is
maintained. Then, a check is made for false intersections. If a
false intersection is found, both the second and second to last
shape point is marked as retained. Further, the pointers are moved
to the next innermost shape points. If a false intersection is not
found, or the pointers cross over one another, the false
intersection check ends.
After performing a false intersection check, a check is performed
to identify inconsistent turning angles at the turning point
between the previous road and the current road. Various embodiments
of road simplification module 697 use one of two alternative
methods for detecting inconsistent turn angles with respect to the
coordinate system oriented along the last segment of the previous
road. The two methods are shown in FIGS. 36A and 36B
respectively.
In the first method (FIG. 36A), a vector between a current shape
point and the previous shape point is formed. The vector is then
compared to the vector between the previous shape point and the
last shape point. If the vectors are not in the same half-plane, or
some other predetermined number of degrees such as quadrants, with
respect to the coordinate system defined by the last segment of the
previous road, then road simplification module 697 retains this
shape point and continues checking at the next shape point.
In the second method (FIG. 36B), a vector is formed between the
first shape point and the current shape point. This vector is
compared to the vector between the current shape point and the last
shape point. If the vectors are not in the same half-plane, or some
other predetermined number of degrees such as quadrants, with
respect to the coordinate system defined by the last segment of the
previous road, then the shape point is retained and the method
continues by checking at the next shape point.
Both the method of FIGS. 36A and 36B loop through the set of shape
points from first to last and perform simple angle checks to
determine whether or not the shape point should be retained. The
first method (FIG. 36A) tends to retain fewer shape points than the
second (FIG. 36B). In some embodiments of road simplification
module 697, the two methods are combined by running the first and
then the second and then retaining all the shape points up to some
average of the two results. A similar turning angle consistency
check is performed by road simplification module 697 at the turn
between the current road and the next road.
While detailed shape information is not necessary for following
most roads, highway on and off ramps are an exception to this rule.
Knowing whether a ramp curves back around to form a cloverleaf or
if it bends only slightly can make it much easier to figure out how
to get on and off the highway. Therefore simplification algorithm
module 697 uses a different simplification criteria for highway
on/off ramps than for the other roads in the route. For ramps, road
simplification module 697 performs a more detailed shape analysis
during simplification. At each interior shape point, the lengths of
the two adjacent segments, and the angle between them is
considered, as shown in FIG. 37. In FIG. 37, for a given shape
point, the two segments adjacent to the shape point have lengths 11
and 12, .alpha. is the angle between these two segments, and
n.sub.1 and n.sub.2 are the number of unsimplified segments that
are represented by each of the current segments. A relevance
measure for the shape point is computed as:
.alpha. ##EQU00002## The higher the relevance measure the more
important it is to retain the point. Road simplification module 697
defines a tolerance value; and if there is at least one shape point
with relevance<tolerance, the shape point with the lowest
relevance is marked as removed. Then, the relevance for all of the
remaining shape points is recomputed; and if possible, another
shape point is removed. This process is repeated until all the
shape points have a relevance larger than the tolerance or all of
the remaining shape points are marked as retained.
The relevance measure is based on two observations. First, sharper
turning angles are more important than shallow turning angles.
Since we measure the smallest angle, .alpha., between adjacent
segments, we use 180-.alpha. in the numerator of the relevance
measure to give higher relevance to the sharper angled roads.
Second, for ramps, turns between shorter segments tend to be more
important than turns between longer segments (see FIG. 38). Thus,
the denominator is the sum of the two adjacent segments. However,
it will be appreciated that removing a shape point causes a segment
to become longer. Therefore if the algorithm were to simply divide
by the sum of the adjacent segment lengths as the process continued
simplifying the ramp, the relevance measures of the remaining shape
points would tend to decrease. Thus, the lengths of the adjacent
segments are normalized by the number of unsimplified segments the
current segment replaces.
Dropping ramps. Entering or exiting most highways requires taking a
short on or off ramp. For long routes (i.e. fifty miles or longer)
that include many highways, showing all the short ramps can clutter
the map with unnecessary detail. However, some ramps, particularly
near the beginning or end of the route, can be very important for
understanding how to follow the route. Therefore, some embodiments
of road simplification module 697 includes a set of heuristics for
evaluating the importance of a ramp. When a given ramp does not
satisfy this set of heuristics, the ramp is dropped. In one
embodiment, this set of heuristics is as follows:
1. Between highway ramps. Ramps between two highways are less
important than those between small roads and highways.
2. First/last ramp. Never drop the first and last ramps on the
route since they are likely to go between smaller, local roads and
the highway.
3. Short routes. Keep all the ramps for routes smaller than a
predefined length cutoff (i.e. 50 miles) or step cutoff (i.e. 20
steps).
4. Long ramps. Keep ramp if it is longer than some pre-specified
minimum ramp length (i.e. 0.1 miles).
5. Short road before/after ramp. If the road immediately before or
after the ramp is shorter than some pre-specified length (i.e. 0.5
miles) keep the ramp.
As in road simplification, the three main problems that road
simplification module 697 seeks to avoid when dropping ramps are
the introduction of false intersections, missing a true
intersection, and the creation of inconsistent turns. To avoid
false and missing intersections the same approach found in the
previously described road simplification process is used by road
simplification module 697. First the set of intersection points
between each pair of roads is precomputed. Before allowing a ramp
to be removed, a check is made to determine whether removal will
add a false intersection to the intersection list, or cause a true
intersection to be missed; and if so, the ramp is not removed.
Ensuring turn angle consistency is slightly different when dropping
ramps than when simplifying road shape. When dropping ramps, road
simplification module 697 checks to make sure that the road
continues to appear to be to the right of the ramp after removing
the ramp. If this relationship does not hold, the turn is
inconsistent and the ramp cannot be removed as shown in FIG. 39.
Note a test for turn consistency does not have to be performed at a
cloverleaf ramp since such ramps essentially form a circle, because
they start and end at the same point, which is the same as the last
point on the road before the ramp (r.sub.1).
To check for turn consistency, road simplification module 697 first
checks if the ramp, which is approximated as a single line segment
between its start and end shape points, turns to the right or the
left of r.sub.1. If the ramp turns to the right then the ramp is
dropped if the direction of r.sub.2 is in the first, second or
fourth quadrant of the coordinate system oriented along r.sub.1.
Similarly if the ramp turns to the left of r.sub.1, the ramp is
dropped if the direction of r.sub.2 is in the first, second or
third quadrant of the coordinate system oriented along r.sub.1.
Similar Optimization Algorithms
While the examples for label optimization and route scale
optimization included refinement of a target function using
simulated annealing, it will be appreciated that the target
functions of the present invention may be refined using any form of
search based refinement algorithm. Representative search-based
algorithm include, but are not limited to greedy algorithms,
gradient descent, simulated annealing, Tabu searches, and A* as
reviewed by Zbigniew et al. in How to Solve It: Modern Heuristics,
Springer-Verlag, Berlin, Germany, 2000, greedy searches A*/IDA*,
simulated annealing and hill climbing (gradient descent) as
reviewed by Russell et al. in Artificial Intelligence: A modern
Approach, Prentice Hall, 1995, and genetic algorithms as reviewed
by Goldberg in Genetic Algorithms in Search, Optimization and
Machine Learning, Addison-Wesley, 1989.
Concluding Remarks
The efficient use of data structures and acceleration techniques is
useful in implementing the methods disclosed in the present
invention. Typically, the search algorithms described herein
require a significant number of iterations to converge, and scoring
is done on each iteration. Often, scoring involves determining
whether various objects in the map intersect, and the costs of
these intersection calculations should be minimized. One way to
minimize the cost of such calculations is to use a two-dimensional
partitioning grid to subdivide the display and reduce the number of
possible candidate objects for any intersection calculation.
It is also possible to significantly reduce the computational
overhead of the search algorithms by performing a simple analysis
before commencing a search. In many cases, the algorithm can
determine the optimal length of a road or the optimal placement of
a label will not detrimentally affect the size or placement of
other roads or labels on the map. Therefore, these attributes can
be assigned a priori thus reducing the size of the search space and
reducing the running time of the algorithm.
References Cited
All cited references are incorporated herein by reference in their
entirety and for all purposes to the same extent as if each
individual publication was specifically and individually indicated
to be incorporated by reference in its entirety for all
purposes.
Other Embodiments
The present invention can be implemented as a computer program
product that includes a computer program mechanism embedded in a
computer readable storage medium. For instance, the computer
program product could contain direction parser 684, road layout
module 686, label layout module 688, and map renderer module 692
(FIG. 6). These program modules may be stored on a CD-ROM, magnetic
disk storage product, or any other computer readable data or
program storage product. The software module in the computer
program product may also be distributed electronically, via the
Internet or otherwise, by transmission of a computer data signal
(in which the software modules are embedded) on a carrier wave.
It will be appreciated that, while reference was made to route maps
that include roads, the present invention encompasses route maps of
any kind. Thus, the route maps of the present invention include,
but are not limited to, hiking trails, campus directions, and
graphical representations of mass transportation networks in
addition to road maps. Further, it will be appreciated that
although reference is made in FIG. 6 to a system for generating a
route map having a client/server format, many embodiments of the
present invention are practiced using a single computer that is not
necessarily connected to the Internet. Further still, it will be
appreciated that the distribution of software modules shown in FIG.
6 is merely exemplary. For instance, embodiments in which direction
parser 684, road layout module 686, label layout module 688,
annotation module 690, map renderer module 692, direction database
694, and geographical landmark database 696 independently reside on
client 622 and/or server 624 fall within the scope of the present
invention.
The foregoing descriptions of specific embodiments of the present
invention are presented for purposes of illustration and
description. They are not intended to be exhaustive or to limit the
invention to the precise forms disclosed, obviously many
modifications and variations are possible in view of the above
teachings. The embodiments were chosen and described in an order to
best explain the principles of the invention and its practical
applications, to thereby enable others skilled in the art to best
utilize the invention and various modifications as are suited to
the particular use contemplated. It is intended that the scope of
the invention be defined by the following claims and their
equivalents.
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